His father Gabriel Léon Mulet was choirmaster of the Basilica of Sacré-Cœur, where his mother Blanche Victoire Augustine Gatin would also play the harmonium; as a boy he sometimes deputised for her.

He studied at the Paris Conservatoire from 1890, where his teachers included Jules Delsart, Raoul Pugno, Xavier Leroux, Alexandre Guilmant and Charles-Marie Widor.

He originally intended to be a cellist, but later served as an organist at Saint-Pierre-de-Montrouge and also taught at the École Niedermeyer and the Schola Cantorum, where he worked with his friend Vincent d'Indy.

Its tones of imposing and embracing calm flood the air of our cathedrals, in the same way that ...stained-glass windows bring down meditation upon the congregation.

Ill-health led Mulet and his wife, Isabelle-Emilie-Marie (née Rochereau) to retire to a convent in Draguignan, where he died in 1967.