Élan Chalon (2018–2021) Between 2018 and 2020, Besson was a member of the
Élan Chalon senior squad. He played 14 games in the
LNB Pro A over two seasons. In the ProA U21 competition, he averaged 18.6 points, 5.8 rebounds, 4.0 assists, and 2.1 steals in 28 games during the 2018–19 season, and 26.0 points, 4.3 rebounds, 4.0 assists, and 2.0 steals in six games during the 2019–20 season. He
led the league in scoring during the 2020–21 season with 19.5 points per game. and earned all-star five and best youngster. His No. 25 jersey was later retired by Saint-Quentin BB.
2021 off-season Besson was courted by several European clubs during 2021, including
Baskonia and
ASVEL, and was in the running for the
NBA draft. He withdrew his name from the draft after being unable to participate in work-outs due to an ankle injury.
New Zealand Breakers (2021–2022) On 23 September 2021, Besson signed with the
New Zealand Breakers of the Australian
National Basketball League (NBL) for the
2021–22 season. In his debut for the Breakers on 4 December, he scored 10 points in an 89–65 season-opening loss to the
South East Melbourne Phoenix. He scored 20 or more points in each of the next three games. He had two 20-point games in March 2022. In 25 games, he averaged 13.9 points, 3.9 rebounds, and 2.5 assists per game. He was sidelined between 9 January and 16 May with a hip injury. His minutes decreased after returning from injury, In 25 games, he averaged 9.2 points, 2.2 rebounds and 2.1 assists per game.
FMP Meridian (2023–2024) On 30 September 2023, Besson signed a two-year deal with
FMP Meridian of the
Basketball League of Serbia and the
Adriatic League. However, on 11 February 2024, he parted ways with the club.
Openjobmetis Varese (2024) On 26 February 2024, Besson signed with
Openjobmetis Varese of the
Lega Basket Serie A.
Manisa Basket (2024–2025) On 4 September 2024, Besson signed with
Manisa Basket of the
Basketbol Süper Ligi (BSL). He averaged 16.6 points, 3.6 rebounds, and 2.9 assists in 29 games in the BSL during the
2024–25 season; and 17.2 points, 4.1 rebounds, 3.2 assists, and 1.4 steals in 14 games in the
Basketball Champions League (BCL).
Tofaş (2025–present) On July 15, 2025, Besson signed with
Tofaş of the BSL, returning to the league for a second stint. He joined the Bucks for the
2022 NBA Summer League. On 6 February 2025, Besson's draft rights were traded to the
New York Knicks in a multi-team trade. ==National team career==