2010-11: Frederik Gauthier played for the College Esther-Blondin Phenix midget AAA team in Quebec. In 37 games he scored 7 goals with 14 assists and had six penalty minutes. The Phenix finished third in the CCM Division and in three playoff games Gauthier was scoreless with no penalty minutes. Gauthier skated for Team Quebec in the Canadian Winter Games; finishing with 1 assist and 4 penalty minutes in six games. He was selected by Rimouski in the third round (40th overall) of the 2011 QMJHL Entry Draft.
2011-12: Gauthier returned to College Esther-Blondin for a second season and was the team's third-leading scorer, finishing with a team-leading 26 goals and 25 assists in 39 games with 28 penalty minutes. Gauthier led the Phenix with 13 goals and had 11 assists in 13 playoff games as the team captured the playoff championship. In the Telus Cup (Canadian midget championships) he scored 2 goals with 9 assist in seven games as the Phenix reached the gold medal game.
2012-13: Gauthier scored at a near point-per-game pace in his first QMJHL season with Rimouski and was selected to represent Canada in the 2013 U18 World Junior Championship. He scored 22 goals with 38 assists and was plus-22 with 26 penalty minutes in 62 games. The Oceanic finished second in the East Division before falling to Gatineau in a first round playoff series. Gauthier had 2 assists and was plus-one with 2 penalty minutes in six playoff games. Gauthier was ranked seventh amongst North American skaters in Central Scouting's mid-term rankings prior to the 2013 NHL Draft, and eighth in the CSS final rankings.