Before playing in the NHL, Dumont played 4 seasons with the Val-d'Or Foreurs of the Quebec Major Junior Hockey League (QMJHL). He was drafted with the 3rd overall pick by the New York Islanders in the 1996 NHL Entry Draft. Dumont had a contract dispute with the Islanders and they traded him and a 5th round draft pick to the Chicago Blackhawks for Dmitri Nabokov in 1998.