Prior to his professional career, Viel skated in 259 games over a four-year span with Acadie-Bathurst and the Sherbrooke Phoenix in the Quebec Major Junior Hockey League (QMJHL). During the four seasons, he totaled 196 points (115 goals, 81 assists), 499 penalty minutes, and a plus-12 rating. In 2017-18, he helped Acadie-Bathurst win the QMJHL championship and the Memorial Cup, recording 23 points in 20 playoff games and 10 points in four Memorial Cup contests. He was awarded the Guy Lafleur Trophy as the league's playoff Most Valuable Player and named to the Memorial Cup All-Star Team.
The six-foot-two, 205-pound native of Rimouski, Quebec, originally signed with San Jose as a free agent on May 29, 2019.