Jean-Luc Godard died peacefully at home in Rolle, Switzerland, on Lake Geneva, his family said.
The family statement said the 91-year-old Godard had multiple illnesses and died from assisted suicide.
The "enfant terrible" of the French New Wave revolutionised popular cinema in the 1960s and spent his career pushing boundaries and reinventing cinematic form.
What greeted audiences in Godard's first feature, the 1960 crime drama Breathless, was the shock of the new.
He played a car thief who idolises Hollywood gangsters. After shooting a police officer, he and his pregnant girlfriend, Seberg, flee to Italy.
As a critic, Godard favoured Alfred Hitchcock and Howard Hawks, and in Breathless, a Humphrey Bogart poster emphasises Belmondo's goal.
With jump-cut editing, a fractured narrative, and actors interacting with the camera, the filmmaker was part of a New Wave in storytelling, which rejected accepted technique.
In 1966, he questioned film grammar until a panellist said, "Surely you agree that films should have a beginning, middle, and end."