Born in Aix-en-Provence, France on 28 October 1686 of noble parentage, Paul Alphéran de Bussan graduated in Bachelor of Theology from the University of Aix in 1705. He soon travelled to Malta and lived with his uncle, Melchior Alpheran de Bussan, a Conventual Chaplain of Obedience of the Sovereign Military Order of Malta. His brother Jean-Melchior Alphéran was also a member of the order of St John and became abbot of Sept-Fons Abbey in 1755. The ship on which the 19-year-old Paul was travelling was caught in heavy storms and had to seek shelter in St. Paul's Bay where he came ashore.
Archbishop Alphéran de Bussan died on 20 April 1757 at his Mdina residence. He was buried in the Cathedral crypt but his heart was interred in the chapel of the seminary he had built. On the initiative of the Cathedral Chapter, a memorial baroque marble slab was installed in the Chapel of the Blessed Sacrament of the Cathedral.