The actor/director was asked at the Cannes press conference for the film if she was worried that Gibson's troubled personal life will affect how audiences respond to his character.
Foster said: "Sure! Well, I think the first order of business is to say who's the right actor for the role. And especially at this point I can't think of anybody else but Mel. He was definitely the first on my list.
"He's somebody that really understands how to handle humour and the lightness and the charm of the character, but also has a deep understanding of the struggles and that he would keep his feet firmly placed in the drama."
She added: "I can't say that of most actors. I think most actors are either in the dramatic end or in the comedy end. Especially actors in the comedic end would have had a hard time resisting going for the comedy for the entire film."
Foster recently admitted that she had "no inkling" of Gibson's personal problems while they were shooting her movie.
> Read our review of The Beaver
> Jodie Foster: 'Beaver is Mel Gibson's best movie
Watch the trailer for The Beaver below: