Born in Saint-François of Madawaska, Camille was the son of Alcime Côté and Anna Marchand. He was a student at the Academy of Hôtel-Dieu in 1923 and 1924 and did his classical studies in Sainte-Anne-de-la-Pocatière. He studied theology at Holy Heart Seminary in Halifax and was ordained priest in his native parish in 1936. Father Côté was the founder and parish priest of Notre-Dame du Sacré-Coeur in Edmundston. Later he was parish priest of Saint-Jacques.