Fest steht und treue die Wacht, die Wacht am Rhein!
We are in the chamber pot, and are about to be shat upon.
—French General Auguste-Alexandre Ducrot
The Franco-Prussian War - known in Germany as the German-French War (Deutsch-Französischer Krieg) or War of 1870/71, and in France as the Franco-German War (Guerre franco-allemande) or "Guerre franco-prussienne" - was the last of three wars that led to the unification of Germany (the first since the Holy Roman Empire had any political power).
There were multiple causes of the war, including but not limited to, a potential sale of Luxembourg to France, the vacancy of the Spanish throne, and the Prime Minister of Prussia modifying and publishing an insulting telegram about a meeting of the French Ambassador. For whatever cause, a dangerously underprepared France declared war on Prussia (and thus the North German Confederation) in July of 1870. These circumstances led the South German states (Bavaria, Baden, Württemberg) to join the side of the North German Confederation.
The result was a 10-month Curb-Stomp Battle as the Prussians decimated the French in all but three battles (where the French won one at Broney-Colombey and fought to a draw in two others), captured the French Emperor, Napoleon III, and unified Germany.
Another result of the war was Germany's annexation of Elsaß-Lothringen (Alsace-Lorraine), which they held until World War One. Moreover, the French had to leave Rome, indirectly finishing the Unification of Italy.
The defeat of Napoleon III led to his fall and the proclamation of the Third French Republic, which continued the war longer than the Germans expected by continually raising new armies even as Paris was besieged. In a bloody epilogue after the signing of the definitive peace treaty French fought French as the forces of the conservative central government put down the Paris Commune, a short-lived revolutionary government which was in control by revolutionary members of the French working class. While short-lived and petty by that time, it would inspire a book by Karl Marx (The Civil War in France) and later Vladimir Lenin to start the October Revolution and create Soviet Union, thus being responsible of communism's first steps as a major power through the 20th century.
By the end of the war, the balance of power in Europe had been completely upended, as France's centuries-long superiority over the rest Europe was brought to an abrupt end. What had once been a chain of small and mid-size powers had, within a year, become the single most powerful state on the continent. Even worse (from the French perspective), Germany was growing stronger, rapidly increasing its population and industry.
This in turn started a chain of events that led to World War I. France, desperate and humiliated, formed a series of alliances in case they ever went to war with Germany again, and Germany did the same. With one exception, all of these alliances became the Allied Powers (France, Great Britain, and Russia and its Baltic allies, as well as the other countries they gathered after the war began) and the Central Powers (Germany and Austria-Hungary, and the countries they gathered). The newly-united Italy was the exception - Italy was in an alliance with Germany, but didn't enter World War I until the Allied Powers offered them parts of the Austro-Hungarian Empire.
Tropes Associated With This War Include:
Awesome but Impractical: The French regarded the Mitrailleuse (a primitive machine gun) as the secret weapon that would win the war for them. Emphasis on secret; security restrictions meant that no-one had a chance to train with the weapon and develop proper tactics. After the apparent failure of the weapon in the face of determined Prussian assults, the French believed that elan (fighting spirit) was more effective than machine guns. The Prussians (who'd been on the receiving end of the Mitrailleuse) decided to concentrate on firepower instead, with tragic results for the French in the beginning of World War One.
Awesomeness by Analysis: The Prussian general staff. By meticulously analyzing railroad networks, their capacities, and schedules, they were able to assemble sufficient men and supplies where they were needed when they were needed to defeat the French, despite the French having a presumably better trained and possibly better equipped army. (French Army was made of professional, long-term service soldiers while the Prussian was made of conscripts. French had better rifles and also early machine guns, although the Prussians had superior artillery.)
The South German armies were in on it, too. One of the first heroes to make headlines through a daring reconnaissance raid was the Württemberg cavalry officer Count Zeppelin (yes, thatCount Zeppelin).
Book Ends: The German Empire was unified and proclaimed in Versailles. The Empire ended there also after World War One.
From a German point of view the proclamation of the German Empire (which would include Alsace-Lorraine) in the palace of the king responsible for taking away Strasbourg etc. from the Holy Roman Empire was also this.
In 1840 French foreign minister Adolphe Thiers tried to escalate the current European political crisis in order to change the Franco-German border, annexing the German territories left of the Rhine to France. He did not succeed as King Louis-Philippe was not as bellicose as Thiers and dismissed him. However, Thiers had not been discreet about the desires of many French to push the borders forward to the Rhine, and this led to a resurgence of German nationalism. Among the various poems declaring readiness to defend the Fatherland against French aggressions was "The Watch on the Rhine" by the otherwise unknown Max Schneckenburger from Württemberg. At the time it passed almost unnoticed, but in 1870, set to a catchy new tune, it became the theme song for the war on the German side. Meanwhile, after the defeat of Napoleon III, Adolphe Thiers became the head of the first government of the Third Republic and as such had to negotiate the peace that changed the Franco-German border in a way rather differently than he had envisaged in 1840.
Also, France's entry into the war meant that the Emperor was forced to recall the expeditionary force he had sent to protect the city of Rome - by then the last the remnant of the Papal States - some years before, thus leaving it free for the Italians to take. The capture of Rome in 1870 completed the process of the Italian Unification.
Boring but Practical: German deployment plans. By careful study of railway time-table and internal organisation of conscription depots, The General Staff managed to plan and then pull a successful deployment of more than 400 thousands of troops from All the Little Germanies in less than two weeks.
Cool Train : The chief German weapon was their trains. It enabled them to get tons of troops to the front in no time. As a bonus it enabled them to use reserves as front-line units without worrying about them falling over with weariness after all the marching.
Cycle of Revenge: The entire war was seen as an important episode in the sequence of wars between "hereditary enemies" France and Germany from the middle ages to World War II.
Eagle Squadron: Giuseppe Garibaldi joined the war against the Prussians in late 1870 and formed his volunteer Army of the Vosges. They mainly fought in the southern regions of France around Dijon until the end of the war.
Freudian Excuse: The defeat led to the rise of revanchism in France. The French Army also amusingly refused to let go of the bright navy blue jackets and red pants they used in 1870 saying that they'd defeat the Germans wearing the same uniforms later. Catastrophic loses in the first months of World War One made them realize that keeping the same highly visible uniforms might cost them a second defeat, and they changed to pale blue (though only after several arguments among themselves).
From Bad to Worse: Relations between France and Germany could not be said to have improved anytime soon after this war.
For bonus irony points: Bismarck believed that even if he were to offer France a moderate peace conditions they would eventually seek revenge for the lost war anyway. Thus, he concluded that if the second war with France is inevitable, he might as well strengthen Germany and weaken France by annexing Alsace-Lorraine. However, it was the annexation of these territories that became the main cause of the enmity between France and Germany in the subsequent decades and possibly it was the reason why the next war between Germany and France became inevitable.
Considering France's foreign policy for two and a half centuries had been to keep Germany weak, Bismarck probably was right.
Of course, he didn't do himself any favors by rubbing salt in the wound and Kicking or Shooting the Dog at just about every step of the war.
Last Stand: The Siege of Paris, which lasted for roughly half the war.
Magnificent Bastard: Otto Von Bismarck, during the four years between the Seven Weeks War and this war he managed to isolate France while gaining an alliance with the Independent Southern German states to finish the unification process. Of course, this is the real life David Xanatos you're talking about.
It is worth mentioning that the only international treaty relevant to defining war crimes at the time was the first Geneva Convention, which dealt with the treatment of sick and wounded soldiers and established protection for facilities marked with the Red Cross. It was only after the war of 1870/71 that international law regarding the use of arms etc. was codified, e. g. through the Hague Convention of 1899. At the time of the Franco-Prussian War there still was quite a bit of leeway of what was considered permissible under the "customs of war", as demonstrated by the wanton destruction during Sherman's March through Georgia and the Carolinas half a decade earlier (which to this day tends to be justified as a "military necessity"). When it came to fighting guerilla war, the French had shown themselves merciless in the wars against the Vendéen royalists in the 1790s and against Spanish guerilleros 1808-1814. And then there was...
The "Bloody Week" that ended the Paris Commune, from which Lenin derived the lesson: "Expect no mercy from the bourgeoisie, so give them none."
Rock Beats Laser: Despite the technological advantage of the French forces (they had far superior rifles, and even an early form of a machine gun), the Prussians still crushed them easily. Partially subverted, as the Prussians had a highly superior artillery, though, leveling down any position held by French infantry, nulling the Chassepot rifle advantage.
The Scapegoat: Marshall Bazaine was a perfect one considering how he behaved during the war (see General Failure above). Everyone, from royalists to republicans to even fellow Bonapartists were happy to put all the blame upon him for the defeat. Which was vastly exaggerating, after all.
The thing that turned him into a scapegoat was not so much that he was put on trial and condemned to death (and immediately recommended for a pardon by the officers who sat on trial over him) for his behaviour during the war, including negotiating with the enemy in a ill-advised bid to preserve the monarchy. It was that most of the others whose failures had led to the French defeat were put on trial. But then another commander whose behaviour could have merited an inquiry was none other than Marshal Mac-Mahon, who was elected president of the Republic after the war.
The Siege: Beside the siege of Paris, there were several smaller ones, in particular the one of the fortress town of Belfort in Lorraine. Here the French forces succeeded in holding the place until the end of the war, which turned their commander, Colonel Denfert-Rochereau, into a national hero. Generaly, sizable part of French forces were besieged by Germans, even further expanding their numerical advantage.
Silly Reason for War: Every technical reason used to declare war or justify it later was this. In reality, Bismarck needed a war against France to convince the other German states to join Prussia, and Napoleon III needed a victorious war against anyone to deflect the criticism gained as a result of the failed French intervention in Mexico. They baited each other, and Bismarck won.
The Spartan Way: The Prussian General Staff which was a number of gifted men who were originally trained to act as strategists that could theoretically institutionalize Napoleonic genius. They were picked from among the best officers, rigorously schooled, trained with war games and staff rides (taking them on a field trip into the country and asking them to evaluate the tactical ramifications of the terrain).
Underestimating Badassery: Prussia was so much underestimated that even King William didn't have proper maps of France at first because he thought he was the one that was going to be invaded.
Emile Ollivier, minister of justice and head of the Imperial French cabinet in 1870 declared in the assembly shortly after war was declared that it unpatriotic and criminal to even consider the possibility of a French defeat. He said it was impossible that the French army could be defeated by the heavy Germans, stuffed as they were with sauerkraut and beer ("gonflés de choucroute et de bière"), those slow-moving crybabies whose flat feet made long marches so hard to them.
Warrior Prince: Both William I of Prussia and Napoleon III of France had aspirations toward this. However, that kind of thing was somewhat outdated and they looked rather out of place in the role. Although William perhaps deserves more credit then he is given. He had two Magnificent Bastards, (von Moltke and Bismarck) working for him and managed to keep them working as a team to optimal level.
The Prussian Crown Prince Frederick (later Emperor Frederick III) commanded the 3rd German Army, which contained most of the South German contingents. His cousin Prince Frederick Charles commanded the 2nd Army, while Crown Prince Albert of Saxony commanded the 4th.
The war started because of the proposed (but rejected) candidacy of a Prussian prince to the throne of Spain, of all things. What if that prince had become King of Spain? Would Spain and Germany have become allies and draw common plans to keep France down?
The French had early machine guns in this war, but deployed them like artillery, making them ineffective.
Given how pivotal the war was, a French victory or the avoidance of the war altogether sets up a whole bunch of interesting and long-range "what if?" scenarios. Most of all, the Second Empire wouldn't have collapsed and France would have remained a Bonapartist monarchy instead of becoming the Third Republic, while German unification under Prussia would have been delayed if not averted. Also twentieth century world history would very likely have run completely differently, given how much this war spawned the national animosities and disruptions to the Balance of Power that in hindsight led up to the World Wars.
Among the crowd at the proclamation of Wilhelm I as German Emperor was a Prussian guards officer, Paul von Hindenburg, later German supreme commander in the final years of World War I and, as president of the Weimar Republic, the man who - begrudgingly and out of other options - appointed Hitler chancellor.
Georges Clemenceau, the man who would head the victorious French government at the end of World War I, witnessed the Paris Commune as mayor of Montmartre.
Zerg Rush: Subtle, but still. Germans were constantly using their numerical advantage (achieved through wide conscription and effective use of railroads) to flank any French forces they met. This and their powerful artillery.
Bombardement d'une maison (Bombing of a house, 1897), most probably the very first film to depict it (and probably the very first war film). It was directed by Georges Méliès (yes, that one)
In the alternate history The Legacy of the Glorious, this war is known as the Hohenzollerns' War, after the reigning dynasty in Prussia (although in TTL's Spain it is called King Leopold's War). Like it happened in Real Life, the most direct cause of the war was the Ems dispatch, but there is a difference: since Leopold of Hohenzollern-Sigmaringen was confirmed as King of Spain before the French caught wind of it, France declares war on Prussia and Spain. War ends even more disastrously for the French, because, apart from Alsace-Lorraine, they also lose the southern department of Rousillon and the Oranesado in north Africa to Spain, as well as paying a greater war indemnization.
Sizable chunk of Victoria: An Empire Under the Sun will be about pouring vast amounts of time and resources either to bring the war or stop/postpone it. The outcome of the war is rather random in vanilla versions of first and second game, but gets brutally historical under expansion packs and mods.
Émile Zola's La Débâcle is set during the war, specifically at the Battle of Sedan and the French civil war in spring 1871.