He was ordained to the priesthood on 1 October 1905, finished his studies in 1908 and then taught canon law at the Seminary of Lyon until 1912.

Pope Pius XII named Jullien, who entered the Society of Saint-Sulpice in 1918, as Dean of the Roman Rota on 30 October 1944.

He was created Cardinal Deacon of S. Giorgio in Velabro by Pope John XXIII in the consistory of 15 December 1958.

Resigning as Dean on 18 December that year, Jullien was appointed Titular Archbishop of Corone by Pope John on 5 April 1962.

He lived long enough to only attend the first two sessions of the Second Vatican Council from 1962 to 1963, and serve as a cardinal elector in the 1963 papal conclave that selected Pope Paul VI.