Born in Colmar to Algerian parents, Boudebouz grew up in the 'Europe' district of the city. At age 10, he joined the junior ranks of local side SR Colmar where he stayed until age 14 when he joined the FC Sochaux-Montbéliard Academy. Boudebouz made his debut for the club's reserve side at the age of 16. On 15 May 2008, Boudebouz signed his first professional contract with the club agreeing to a three-year deal tying him to the club until 2011.
On 4 October 2008, Boudebouz made his first team debut for Sochaux, starting in a league match against Nice. On 8 November 2008, he scored his first career goal, the winner in a 2–1 victory against Le Mans.