Petit was born in Poitiers, the son of a professor of the khagne. He studied literature and music in Paris and studied literature at the Sorbonne. He was admitted to the Paris Conservatoire in 1942, where he studied at the Conservatoire de Paris. His teachers included Georges Dandelot for music analysis, Nadia Boulanger for harmony, Noel Gallon for counterpoint and fugue, and Henri Busser for composition.
In 1946 he won the Premier Grand Prix de Rome with the lyrical scene Le jeu de l'amour et du hasard, which was performed in the same year by the orchestra of the Cadets du Conservatoire under the direction of Claude Delvincourt.
From 1951 Petit taught the history of civilization at the Conservatoire de Paris and the Ecole polytechnique. In 1960, he began working for the Office de Radiodiffusion Television Francaise. At first he was head of light music, and then from 1965 he was musical director. Among others, he produced music for accords parfaits, contre-ut, Presto, Figaro ci figaro la.
In 1963 he was appointed director of the Ecole normale de musique de Paris, succeeding Alfred Cortot and working alongside such musicians as Nadia Boulanger, Georges Dandelot, Alfred Desenclos, Norbert Dufourcq and Marguerite Roesgen-Champion. He held the position for 35 years, when he was succeeded by Henri Heugel. His students included Roger Bellon.