Rhéaume played for the Sherbrooke Jofa-Titan squad in the League Régionale du Hockey au Féminin in the province of Québec. She was the first female goaltender to play for a boys' team in the 1984 Quebec International Pee-Wee Hockey Tournament.
Rhéaume was signed to the Trois-Rivières Draveurs in the Quebec Major Junior Hockey League, one of Canada's top junior ice Hockey leagues, for the 1991–92 season, becoming the first woman to play in a men's Major Junior Hockey game.
The 1st and only woman ever to play in a National Hockey League / NHL exhibition game. In 1992, Rhéaume tried out for the Tampa Bay Lightning; this was the first time a woman tried out for an NHL team. She played one period in an exhibition game against the St. Louis Blues on September 23,, allowing two goals on nine shots, and played in another exhibition game against the Boston Bruins in 1993.
She spent five years in professional minor leagues, playing for a total of seven teams. The Atlanta Knights of the International Hockey League / IHL. Her first appearance against the Salt Lake Golden Eagles marked the first time a woman appeared in a regular season professional Hockey game. She played for seven different teams between 1992 and 1997, including Atlanta, the Knoxville Cherokees, Nashville Knights, the Las Vegas Aces, the Tallahassee Tiger Sharks, Las Vegas Thunder, and the Reno Renegades, appearing in a total of 24 games.
Rhéaume also played on the Canada women's national Ice Hockey team, winning Gold Medals at the IIHF Women's World Championship in 1992 and 1994, and the Silver Medal at the 1998 Winter Olympics.