Delpy was born in Paris, the daughter of Albert Delpy and Marie Pillet, both of whom were actors in both feature films and in the avant-garde underground theater; her father grew up in Vietnam, Cambodia and West Africa, where her paternal grandfather worked in administrative positions in the French colonial government. Encouraged to perform by her bohemian-minded parents, Delpy made her stage debut at the age of 5, and at 14 obtained a role in the film Detective, directed by Jean-Luc Godard.
Two years later, Delpy was cast in the title role in the film La Passion Béatrice, and used the money she earned to pay for her first trip to New York City. Delpy continued making regular trips to New York over the next few years, before finally moving there in 1990.
