The Valencia loanee was unveiled at a press conference in Milan on Friday, having completed his temporary switch in the current transfer window with an option to make the deal permanent.
The Frenchman, who has 26 caps for his country, is focused on having a positive spell with the Rossoneri in a bid to be selected by Didier Deschamps for the World Cup.
"Should I play well here, I hope to go to the World Cup but you have to go step by step. Now I just think about Milan," he told reporters.
"It's a fantastic club with tradition. I just want to work a lot and repay the faith.
"Of course I think of the French national team. Milan is one of the most important clubs in the world and I think if I work hard and earn my place, of course I can aspire to the national side."
Milan have brought in the likes of Keisuke Honda and Rami on a budget this transfers window and club chief Adriano Galliani explained his preference for bringing players in from overseas, rather than scouring Serie A.
"We monitored the situation in Europe [with Rami and Honda] and as soon as we saw a glimmer of hope we arrived first," he said.
"There are many deals abroad. I would say that abroad is much more dynamic than the Italian scene."