The Duchy of Grand Fenwick, a miniscule nation covering about 15 and 3/4 square miles located somewhere in the French Alps (but which, due to a quirk of history, nonetheless speaks English) remains prosperous thanks to its sole export, Pinot Grand Fenwick wine. When a Californian imitation forces Pinot Grand Fenwick out of the American market (its largest market) and the tiny Ruritania's complaints to the American government go unanswered, the Duchy government decide that the only course of action is to declare war on the United States — after Grand Fenwick's inevitable defeat, the Americans, being a very strange people, will pour in massive amounts of reconstruction aid, solving all of the Duchy's problems. The Duchess of Fenwick, Gloriana XII (Peter Sellers), the Hereditary Prime Minister, Sir Rupert of Mountjoy (also Peter Sellers), and the Head of the Loyal Opposition send an invasion force of twenty longbowmen in chainmail to invade America under the command of the Hereditary Forest Ranger and Hereditary Field Marshal and Grand Constable of the Army, Tully Bascombe (Peter Sellers again).
When the Grand Fenwick invaders arrive in New York, they find the streets deserted — the city is in the middle of an air raid drill after America's announcement of the invention of the Q-Bomb, an ultimate weapon that "makes the H-Bomb look like a firecracker." After the invasion force tries taking a shortcut through Central Park to get to the Armory (hoping to find someone there to surrender to), a pair of civilian decontamination workers mistake the chainmail-clad Fenwickians for extraterrestrials and flee, leaving behind their truck, which the invaders borrow. The invaders, taking a wrong turn, end up at the New York Institute of Physics by mistake, where they encounter and capture the Q-Bomb's inventor, Dr. Kokintz (David Kossof), his daughter Helen (Jean Seberg), and a working model of the Q-Bomb (a Blinkenlights-covered, over-sized football that buzzes frighteningly as a warning if jostled, since it can go off on a hair-trigger), followed by a general and four New York policemen sent to investigate rumors of the "alien" invaders.
Returning home, the invasion force dismays the Duchy (which had been gearing up to welcome the victorious Americans) with the news that Grand Fenwick has defeated the United States and captured the most destructive weapon in the world. Stress mounts worldwide and among the Duchy government as every country in the world offers to help defend Grand Fenwick (and take possession of the Q-Bomb) from America and America struggles to figure out what to do (ultimately deciding to surrender). After Sir Rupert and the Opposition Leader resign and make a failed attempt to return the Q-Bomb to the Americans, Tully becomes Prime Minister, negotiates a peace treaty with the United States (the terms of which include an end to the manufacture of the "Pinot Grand Enwick" imitation wine, a million dollars, and a worldwide nuclear disarmament enforced by a new League of Little Nations), and marries Helen.
At the end of the movie, Dr. Kokintz insists on checking up on the Q-Bomb, which has been jostled quite a bit over the last few days. Accompanied by Helen and Tully, he discovers that the bomb was a dud all along. The three leave the room, agreeing amongst themselves to tell no one. And then a mouse crawls out of the Q-Bomb, which flickers back to life.