Mazé finished second to Russian grandmaster Evgeny Alekseev in the Master open tournament of the Biel Chess Festival in 2008, and followed it up with fourth place at the French championship (won by Étienne Bacrot).

This qualified him from the French national team at the Olympiad in Dresden that year, where he scored 3½/6.

In 2010, he finished in a tie for first place in the Master open at Biel with Alexander Riazantsev, Nadezhda Kosintseva, Vitali Golod, Leonid Kritz, Sébastien Feller and Christian Bauer, finishing seventh on tiebreak.

[2] Mazé shared first place with Étienne Bacrot in the London Chess Classic FIDE Open in 2016.

[3] The next year, he tied for first again in the same tournament, this time with Gabriel Sargissian and Hrant Melkumyan.