The 28-year-old has played for Les Bleus in Didier Deschamps's first two games in charge and is delighted to be back playing for his country.
"It felt good to play, but more important than individual performances is the victory of the team," Mavuba told L'Equipe.
"Today, talk of a bid for the France captaincy is premature, even if it would be a great honour. I will try to ease myself into this team rather than steal the headlines.
"Relaying between coaches and teammates comes naturally from my time with Lille, but here there are already players in designated positions. For the time being, I consider Hugo Lloris my captain."
Mavuba joined Lille from Villarreal in 2008.