Bousquet began his career at Lézignan Sangliers. He moved to Catalans Dragons and made his debut in 2012. In early 2013 he was involved in a controversial incident during a match against Salford when he knocked Théo Fages unconscious with an illegal challenge, receiving a red card and subsequently being banned for four matches.
On 30 May 2015, Bousquet signed an extension to his Catalans contract.[6]
Bousquet played in all three French matches of the 2014 European Cup campaign.
Bousquet appeared for France again in the 2015 European Cup tournament. He also played for France in their mid-tournament test-match against England. He was a part what was considered a 'weakened' French side due to injury and it showed with an appalling showing against their opponents.[11]
Bousquet played in France's lone international fixture of 2016, an end of year test match against England in Avignon.