But there was also widespread vitriol online from supporters of Heard. Journalist Eve Barlow, a friend of the actress, accused Cannes of having a "history (of) supporting rapists and abusers".
Depp won a defamation trial against Heard last year but lost a previous libel case in London and remains a toxic figure for many.
The 59-year-old actor dismissed the years of newspaper coverage as the "stuff you stuff in your shoes or line your parrot cage with".
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."
