President Nicolas Sarkozy paid tribute to what he called "an immense creator who left his mark on the art of dance in the 20th century".
Sarkozy in a statement expressed his condolences to "Zizi Jeanmaire, his wife and his muse, with whom for 50 years he formed a legendary couple that was dear to the hearts of all French people".
Petit created around a hundred dramatic ballets, which often combined fantasy elements with contemporary realism, including "The Strolling Players" and "Carmen", and did the choreography for several French and US films.
French Culture Minister Frederic Mitterrand said Petit was "one of the major choreographers of the 20th century".
"With his muse Renee Jeanmaire, or Zizi, with whom he formed a legendary couple, he wrote some of the most beautiful pages of contemporary music hall," the minister said.
Jeanmaire performed in many of his creations.
Petit last year returned to the Paris Opera Ballet with three of his favourite ballets, "The Young Man and Death," which was based on a libretto by Jean Cocteau, "Le Rendez-Vous" and "The Wolf".
"Each time he came it was like the return of the prodigal son," said Brigitte Lefevre, artistic director of the Paris Opera Ballet where Petit trained as a dancer.
Petit was born on January 13, 1924 in the northeastern Paris suburb of Villemomble to an Italian mother and a father who ran a cafe in Les Halles, the traditional central market of the city.
At the age of 10 he started attending the dance school at the Paris Opera Ballet.
He served as artistic director of that institution for a few months in 1970 but gave up the job to buy the Casino de Paris concert hall in which he staged revues that starred his wife
From 1972 to 1998 he was director of the Ballet de Marseille.
His later choreographic creations include "Pink Floyd Ballet", to the music of the iconic rock group.
Petit had lived in Geneva for the last 10 years. He has one daughter, Valentine.
Petit's memoirs, titled "J'ai dansé sur les flots" (I Danced on the Waves), were published in 1993.