This is the first child for Cotillard and her actor-director boyfriend Guillaume Canet, who have been together since 2007. The couple co-starred in 2003's "Love Me If You Dare" and Canet recently directed Cotillard in "Little White Lies."
Their baby Marcel was born Thursday night.
"Mother and baby are fine," an insider told People.com. "[Cotillard is] very happy."
Cotillard won a Best Actress Oscar for her work in "La Vie En Rose." She has also appeared in "Inception" and "Nine."