Born in Seclin, Dumont started his career at Lille OSC in 2003. He came to the forefront thanks to the departure of Benoît Cheyrou. Having signed his first contract during the 2002–03 season, he enjoyed a good start to the season before a broken ankle led to a season of merely training and little else. Claude Puel, who was then the coach of Lille, decided to use Dumont as a backup for Mathieu Bodmer and Jean Makoun in midfield. He played for Lille over the eight seasons until 2011, a year in which the team won the league title, making 138 appearances and netting 9 goals.
On 18 July 2011, Dumont moved to the relegated Ligue 2 club AS Monaco FC on a three-year contract.