During the Algerian War Feltin strongly supported the French army and dismissed allegations of widespread torture as "exaggerations". He accused people who spread such information with undermining national unity and insulting the honor of the army. 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. Feltin denounced the use of torture in 1960 but continued his opposition to the legalization of conscientious objection in France, rejecting objections to the war by certain French Catholics. In anti-war Catholic circles, Feltin's actions were met with displeasure.[2]
He attended the Second Vatican Council from 1962 to 1965. He resigned as Paris' archbishop on 21 December 1966.
After the first meeting between Church and Freemasonry which had been held on 11 April 1969 at the convent of the Divine Master in Ariccia, he was the protagonist of a series of public handshakes between high prelates of the Roman Catholic Church and the heads of Freemasonry.[3]
In 1959, Feltin requested of the Holy Office that the Worker-Priest movement be revived, albeit under strict controls; his request, however, was denied.[5]
In 1963, Feltin denied Édith Piaf a religious funeral due to her controversial life.[6] However, on 10 October 2013, fifty years after her death, the Roman Catholic Church gave Piaf a memorial Mass in the St. Jean-Baptiste Church in Belleville, Paris, the parish into which she was born.