[4] After his second season with Kalpa, in which he led the team with 41 points in 55 games, Texier was assigned to the Blue Jackets' American Hockey League (AHL) affiliate, the Cleveland Monsters.

[6] He scored his first NHL goal the following night against the Ottawa Senators in the team's final regular season game on 6 April.

With the following 2020–21 season delayed due to the COVID-19 pandemic, Texier was originally loaned to join his former Finnish club, KalPa, on 8 September 2020.

At the 2017 U18 World Championship he helped the French under-18 team win the tournament, earning promotion to the elite division for the first time in their history.

[15][16] He was expected to make his debut for the French senior team at the 2017 World Championship, which was co-hosted in Paris and Cologne, but a shoulder injury kept him out.

Fabrice played four games in the 1986–87 QMJHL season with the Laval Titan, spending the rest of his career in France, mainly with the Brûleurs de Loups.