Rosay was born Françoise Bandy de Nalèche in Paris, the illegitimate daughter of Marie-Thérèse Chauvin, an actress known as Sylviac.

She originally planned to become an opera singer, and in 1917, won a prize at the Paris Conservatoire and made her debut at the Palais Garnier in the title role of Salammbô by Ernest Reyer.

She appeared in several films under her husband's direction, including Le Grand Jeu (1933), Pension Mimosas (1934), La Kermesse héroïque (Carnival in Flanders) (1935) and Les Gens du voyage (1937).

Rosay spent the duration of World War II in England and Switzerland, where she taught acting classes at the Conservatoire de Genève.

In Hollywood, she co-starred with Charles Boyer, Maurice Chevalier and Buster Keaton and worked with directors such as William Dieterle (September Affair, 1949), Martin Ritt (The Sound and the Fury, 1958), Ronald Neame (The Seventh Sin, 1956), and Peter Glenville (Me and the Colonel, 1957) with Danny Kaye.