Cotillard was a favorite in the annual Cesar competition, comparable to the Oscars, after critics agreed that she captured the soul of France's queen of song in the film.
The award for best movie went to "La Grain et Le Mulet" (The Grain and the Mule), which centers on a Tunisian immigrant family in the southern French town of Sete. It took four Cesars, including a best director award for Abdellatif Kechiche.
He repeated a a 2005 winning streak for his film "L'Esquive" (Games of Love and Chance), which won four Cesars.
The best actor Cesar went to Mathieu Amalric for "Le Scaphandre et le Papillon" (The Diving Bell and the Butterfly). He plays a French magazine editor whose stroke leaves him paralyzed in the adaptation of Jean Dominique Bauby's memoir.
The Cesar for best foreign film went to "The Lives of Others" by German director Florian Henckel von Donnersmarck, the story of a Stasi secret service officer in former East Germany with conflicting loyalties. The film won a best foreign language Oscar last year.
"Persepolis," the animated movie by Iranian-born Marjane Satrapi was named best first film.