Henry going into his parents' bedchamber and waking them up to say:
Henry: Mother, Father, I want to build a University, with the largest library on the continent, where anyone can study, no matter their station!
King Francis: All right... Who are you... and what have you done with my son?
Henry: Oh, and I want to invite the gypsies to the ball!
Even funnier if you catch the King's easy to miss line just before Henry wakes him up:
King Francis: (sleepily): Off... with his head...
The Queen advising her son to choose his spouse carefully, because "Divorce is something they only do in England."
That line is funny no matter if you know the history behind it, but if you do, it gets so much better. Henry VIII was a contemporary, if you take the film's chronology as correct. He'd already married his first wife, Catherine of Aragon, and set her aside while treating her horribly because he wanted Anne Boleyn. The fight to divorce Catherine and marry Anne went all the way up to the Pope, who told Henry the church wouldn't allow it. Henry's response was "Fine. We don't have to be in your stupid church. I'll make my OWN", thus beginning the Anglican church and altering England forever - over a divorce.
The events portrayed are semi-historical, there not really being a good explanation for which Francis, Henry and Marie they could possibly be. There WAS a King Francis whose son was called Henry, but his consort was Claude, not Marie. And there was another Francis, whose consort was Mary, which would logically be Frenchified as Marie... but that would be Mary, Queen of Scots who famously outlived a few husbands before dying herself. However, if you take a pinched, alternate view of things, there are LOTS of English Marys who would be available to marry a French king in this alternate universe and when this troper first saw the film, I assumed that Marie was an English princess who was sister/cousin/niece to the oft-divorced Henry VIII and wishing she were so lucky... ESPECIALLY given the look Francis gives her when she says it.
After Danielle punches Marguerite, the baroness orders her whipped. Later, Jacqueline is dressing her wounds and takes a moment to admire her stepsister - "I shall never forget the way Marguerite's feet went up over her head like that!"
(after an enormous shrieking tantrum) "...There was a bee."
Gustave fainting after meeting Leonardo Da Vinci, his idol.
Believing he met his idol. Leonardo was behind and to the side of him.
When a couple of sympathetic servants are trying to get into a locked room to help Danielle, Leonardo Da Vinci comes along and removes the pins from the hinges, and when the servants declare this to be a stroke of genius:
Leonardo da Vinci: I shall go down in history as the man who opened a door!
Henry's interrupted wedding to Princess Gabriela, who can't do anything but sob and plead in her mother tongue is half this, half Crosses the Line Twice. It's even better when Henry calls off the wedding and lets Gabriela go to the guy she loves (one of the courtiers)... and then the Spanish Royal couple start bitching at each other... and in Spanish too.
Spanish Queen: ¡Es tu culpa! (It's your fault!)
Spanish King: ¡Es la tuya! (It's yours!)
Most particularly, Henry's contemplative pause and rueful little laugh as he recognizes the ridiculousness of the whole thing.
"And I thought I had problems..."
This really snarky piece of dialogue between the King, Rodmilla and Jacqueline when Rodmilla and Marguerite are called upon the Royal Couple's presence and unmasked as Danielle's abusers.
The King: Good Lord! Do they always behave like this?
Jacqueline: Worse!... Your Majesty.
Baroness Rodmilla de Ghent: Jacqueline, darling, I should hate to think you had anything to do with this.
Jacqueline flirting with Laurent at the ball. At least something good came from masquerading as a horse.
Then Horse Laurent ate a carrot.
"Milady, you may take anything you can carry!" After a moment's pause, Danielle hefts Henry over her shoulder and begins to walk off with him, leaving the gypsy leader first flabbergasted. He then laughs uproariously and calls for her to come back so he can give her a horse.
And Henry's resigned shrug to the gypsy as he gets picked up. "Yep, this is my girlfriend."
"Were there just the two of you?" "...And the chicken, Your Highness!"
"What about our breakfast?" "You have two hands. Make it yourself."
"I'm visiting a cousin." "Who?" "My cousin."
The laundry lady knocking Rodmilla and Marguerite into the laundry pool at the end, saying that their arguing is getting on her nerves.
At the beginning, the sight of Gustave covered in mud from when Danielle beat him up.
Danielle throwing apples at Henry - and not just throwing them but beaning him in the head and knocking him right off her father's horse.
Danielle: [*horrified] Forgive me, Your Highness. I did not see you!
"The only throne I want her (Marguerite) sitting on is the one I have to clean every day!"
"Engaged? To a Belgian?" What makes it funny is Henry's extra emphasis on Belgian — as if it's bad enough that Danielle's (supposedly) engaged to someone else, but it being to a Belgian is somehow even worse.
During that time period (1512 according to the novel), Belgium was a collection of provinces that labored under the rule of the French monarchy. Relations were never good and they revolted several decades later. So having the woman he loves engaged to a Belgian would be seen as a serious affront.
Henry has raced off to Pierre le Pieu's house, ready to rescue Danielle. No doubt he was pumping himself up to assault the house, challenge Pieu to a duel, or whatever. He's stopped short at the sight of Danielle walking out under her own power. He must've been thinking "Well, this is awkward..."