"Anne died this morning. She had been very sick," her brother Pierre Wiazemsky, an actor, told AFP.
Wiazemsky, 70, made her screen debut as an elfin 19-year-old in "Au Hasard Balthazar", Robert Bresson's classic 1966 film about a mistreated Christ-like donkey, before meeting Godard -- then at the height of his fame -- a year later.
They married during the shooting of his 1967 film "La Chinoise", in which Wiazemsky plays a member of a Maoist revolutionary cell.
Her grandfather, the Nobel Prize-winning novelist Francois Mauriac, opposed the marriage to the radical maker of "Breathless" and "Contempt", who was 17 years her senior.
But the French student uprising and strikes of May 1968, in which Godard became a major player, overwhelmed them.
"The further it went on, the more our paths diverged," Wiazemsky told AFP in an interview this year.
She later wrote a book about their short-lived relationship, "Un An Apres" (One Year Later). It was the basis of a recent comedy about Godard, "Le Redoutable" (Redoubtable), by the Oscar-winning director of "The Artist", Michel Hazanavicius.
One of Wiazemsky's last public appearances was at the movie's premiere at the Cannes film festival in May.
She appeared in more than 35 films, most memorably alongside Terence Stamp in Pier Paolo Pasolini's "Theorem", which was initially banned for obscenity in Italy in 1968 for its story of a lost disciple of Christ who seduces a whole family.
But she gradually set aside acting for writing, publishing more than a dozen novels. Her final book, "Un Saint Homme" (A Holy Man) came out last year.