Fiset was drafted in the 2nd round 24th overall in the 1988 NHL Entry Draft by the Quebec Nordiques. He played thirty-four minutes in 6 games in his rookie season with Quebec, playing behind Ron Tugnutt, as well as a plethora of other goalies who got time that season. Fiset got his first NHL victory on October 29, 1991, against the Winnipeg Jets in Le Colisee de Quebec, with a score of 7–2. Over the next few years, Fiset bounced from the NHL to the Nordiques' minor league affiliates, slowly gaining more and more time in net for the Nordiques. After the 1992–93 season, Ron Hextall was traded to the New York Islanders, opening the door for Fiset to be the starter. Fiset did not disappoint. Within 2 years, Quebec finished first in the Eastern Conference, during the shortened 1994–95 lockout season. When Quebec moved to Colorado, the future looked bright for Fiset and the Avalanche. This soon changed. He split time with Jocelyn Thibaultin the beginning of the season. However, when Patrick Roy was traded to Colorado from Montreal, Fiset became his backup. Fiset was a part of the 1996Stanley Cup winning team, but was traded to the Los Angeles Kings a few days later. He was the Kings' first choice starter until the 1999–2000 season, where he split time with Jamie Storr. In the 2000–01 season a knee injury, inflicted from a collision with Mighty Ducks of Anaheim's Dan Bylsma, kept him out of twenty-five games then followed by a second knee injury that kept him out for another thirty-one games reducing Fiset to only 7 games. After the Kings acquired Félix Potvin to cover he then effectively lost his starting position and although still hampered by his knees was traded at the back end of the 2001–02 season to the Montreal Canadiens, but only played 2 games. With persistent health issues over the previous two years and loss of form Fiset announced his retirement on September 9, 2002.
International play
Fiset played in the 1989 Junior World Championships, as well as in 1990. In '89 Canada finished fourth, and Fiset was pulled in a 7–1 drubbing by the Soviet Union after giving up 6 goals. He followed this up in 1990 with a great showing. Team Canada had a gold medal finish and the IIHF Directorate Top Goalie Award. He played in 2 games during Canada's 1994 gold medal victory.
Goalie masks
Fiset wore one of the most recognizable goalie masks in the history of the NHL. The design is an ice wall that is supposed to be related to the Quebec Nordiques' igloo logo. There was also the fleur-de-lis, the Nordiques alternate logo, on each ear of the mask. While he played for the Los Angeles Kings, he also donned a memorable mask with the face of King Tut as it appeared on the Pharaoh's tomb.
