Francis Chapelet started studying the organ at the école César Franck, under the direction of Édouard Souberbielle.
He later studied at the Conservatoire de Paris where he won the first prizes in harmony (with Maurice Duruflé as professor), and organ and improvisation (with Rolande Falcinelli) in 1961.
In 1964, he was named co-holder of the organ of the Saint-Séverin in Paris, a position he held for twenty years, and of which he remains an honorary member.
He was a member of the two organ commissions (classified, unclassified) of the Ministry of Culture.
He is also honorary organist of San Giovanni dei Fiorentini in Rome.