Barrère made his Grand Slam main-draw debut at the 2016 French Open, where he received a wildcard, but lost to David Goffin in the first round.

In 2019, he succeeded to qualify and reach the second round of two Grand Slams 2019 Wimbledon Championships and the US Open, defeating Alexander Bublik and Cameron Norrie respectively, and also reach the second round of the 2019 French Open as a wildcard where he lost in four sets to 10th seed Karen Khachanov after winning the third set 6–0.

He reached the final of the 2021 Play In Challenger in Lille for a third time in his career at this tournament but lost to Zizou Bergs.

He made his Masters 1000 debut at the 2023 BNP Paribas Open where he lost to wildcard Jack Sock.

At the 2023 Miami Open he recorded his first Masters win over qualifier Roman Safiullin having never won a match at this level.

He then defeated 11th seed Cameron Norrie in straight sets for his biggest and first top-20 win to reach the third round of a Masters for the first time in his career.

At the Italian Open he reached the third round defeating Brandon Nakashima and upsetting eleventh seed Karen Khachanov.