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."
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 entire wedding. "Azuquita! Azuquita!"
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..."
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 and then laughing uproariously and calling 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."
"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.