A native of Quebec, Gauthier developed in its local minor ice hockey programs and intended to pursue a collegiate career rather than the QMJHL. After his selection by the Océanic in the QMJHL and Youngstown Phantoms in the United States Hockey League, he was encouraged by Sidney Crosby to pursue a career in his native province. During his tenure with the team, Gauthier competed for Team Canada at various international tournaments. He won a gold medal at the 2013 IIHF World U18 Championships and 2015 World Junior Ice Hockey Championships.