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. He played in the
2018 Challenge Cup Final victory over the
Warrington Wolves at
Wembley Stadium. On 9 October 2021, Bousquet played for Catalans in their
2021 Super League Grand Final defeat against St. Helens. On 14 October 2023, Bousquet played in Catalans
2023 Super League Grand Final loss against
Wigan. ==International career==