The French Football Federation (FFF) confirmed the news on its website on Thursday.
Hidalgo also took France to the 1982 World Cup semi-finals, losing to West Germany on penalties, but the 1984 tournament on home soil was an emotional highlight with French playmaker Michel Platini grabbing nine goals in five matches to finish as the tournament's top scorer.
The creative midfield quartet marshalled by Platini with Alain Giresse, Jean Tigana and Luis Fernandez was acclaimed as the "Magic Square" (Carre Magique).
"The federation, our football is in mourning," said FFF president Noel Le Graet.
"Michel Hidalgo is one of the greatest names in French football...through his footballing philosophy, his personality, his exemplary passion, he contributed to our sport shining internationally and its popularity in France."
(Reporting by Alan Baldwin in London, editing by Ed Osmond)