He also attended the Seminary of Saint-Sulpice in Paris, the Pontifical Gregorian University in Rome, and the Catholic Institute of Paris. Gouyon was ordained to the priesthood on 13 March 1937, and finished his studies in 1939.
He served as Archbishop of Rennes from 1964 to 1985, and was elevated to the cardinalate in 1969. After serving in the French Army during World World War II from 1939 to 1940, he began pastoral work in Bordeaux, serving as pastor of Montussan and of Beychac (1940–1944), chaplain of the lycée Michel-Montaigne (1944–1951), and vicar general of the archdiocese. He was raised to the rank of Domestic Prelate of His Holiness on 6 April 1955.
On 6 August 1957, Gouyon was appointed Bishop of Bayonne by Pope Pius XII. He received his episcopal consecration on the following 7 October from Archbishop Paul Richaud, with Archbishop Joseph Martin and Bishop Louis Guyot serving as co-consecrators, in the Cathedral of Saint-André.
Gouyon attended the Second Vatican Council from 1962 to 1965, and was promoted to Coadjutor Archbishop of Rennes and Titular Archbishop of Pessinus on 6 August 1963. He succeeded Clément-Emile Roques as Archbishop of Rennes on 4 September 1964.
Pope Paul VI created him Cardinal-Priest of Natività di Nostro Signore Gesù Cristo in via Gallia in the consistory of 28 April 1969. Gouyon was one of the cardinal electors who participated in the conclaves of August and October 1978, which selected Popes John Paul I and John Paul World War II He was also named the national president of Pax Christi.
He resigned his post as Archbishop on 15 October 1985, after a period of twenty-one years, and lost the right to participate in conclaves upon reaching the age of eighty on 24 October 1990.
Member of Pax Christi (past president, French section).