Born in Delle, Territoire-de-Belfort, Maurice Feltin studied at the Seminary of Saint-Sulpice in Paris before being ordained a priest on 3 July 1909.

He received his episcopal consecration on 11 March 1928 from Cardinal Henri-Charles-Joseph Binet, with Bishops Paul-Jules-Narcisse Rémond and Jean-Marcel Rodié serving as co-consecrators.

He was created Cardinal Priest of Santa Maria della Pace by Pope Pius XII in the consistory of 12 January 1953.

During the Algerian War Feltin strongly supported the French army and dismissed allegations of widespread torture as "exaggerations".

In the fall of 1959, he met with General Jacques Massu, a leading advocate for the use of torture, reassuring him that the Church supported the army.