After several months of illness, Miller died in Paris on Wednesday evening, his producers have announced.
The Cannes festival Twitter account immediately paid tribute to him, declaring Thursday “a day of sadness”.
Miller won the jury’s special prize in 1998 for La Classe de neige (Skiing lessons).
His first feature film was La meilleure façon de marcher (The best way to walk) in 1976.
His first cinema hit was 1981’s Garde à vue (Detained for questioning), which starred French cinema legends Lino Ventura and Michel Serrault.
In a younger generation, he worked with Charlotte Gainsbourg in 1988 on La Petite voleuse (The little thief) and Cécile de France on 2007’s last film Un secret (A secret).
Miller started working in film while in the army and, before directing his own films, Miller worked with New Wave pioneers Jean-Luc Godard and Robert Bresson.
Miller family was Jewish and films such as A secret and L’accompagnatrice (The accompanist) referred to the experience of France’s Jews during World War II.