No. The place is the stadium of Roland garros but the complete name of the tournament is "Internationaux de France de Roland Garros" in French, and it is always referred as Roland Garros.
French Open, or his french version, Open de France, does not exist really. It's the name of a golf tournament.
I just thought it was odd to call Roland Garros the french open while Wimbledon was not named the english open.
I think it's more of a decriptive term than an official name