Reviews of the film itself were mixed, with The Guardian saying Depp gave a "purring and peculiar" performance.
Depp speaks French throughout and said he was stunned when director Maiwenn, who also plays the lead role, asked him to join the film.
"I thought it was very brave of her to choose a hillbilly from Kentucky as Louis XV," said Depp, who lives much of the year in France.
Maiwenn, who herself may face criminal proceedings after grabbing the hair of a Paris journalist and spitting in his face, said she had no doubts about choosing Depp for the role.
"It was someone I had to kiss, so I preferred to have an actor who is sexy," she told reporters.
"And he knew an enormous amount about French history. He knew a lot more than me about Louis XV."
