The actress, singer, screenwriter and director was arguably best known for starring in the François Truffaut film Jules et Jim in 1962.
Moreau was found dead at her home in Paris, the district’s mayor told the AFP news agency.
Paying tribute, French President Emmanuel Macron said Moreau had “embodied cinema” and was a free spirit who “always rebelled against the established order”.
Born on 23 January 1928 in Paris, Jeanne Moreau spent part of her childhood in Vichy before returning to settle with her family in Paris. Her father ran a brewery in the 9th arrondissement and her mother, of British origin, was a dancer at the Folies Bergère.
An iconic of French cinema who reached the height of her fame during the 1960s; she was the recipient of multiple lifetime achievement awards, including a BAFTA fellowship was awarded to her in 1996.
She was a friend and collaborator of many other of the most recognisable figures in French cinema, including Jean Cocteau, Jean Genet and Marguerite Duras.
She won a number of awards including the Best Actress prize at Cannes for Seven Days… Seven Nights in 1960.
She worked with Orson Welles on several films and won the Bafta Award for best foreign actress for Viva Maria! in 1967.