Was it the Bataclan theater?

No. The Bataclan is (was, anyway, and perhaps will be again as they are planning to rebuild it) more a venue for concerts and the like than an actual theater where plays are produced. At the time of the film, it was actually being used as a cinema rather than a concert hall but this changed again afterwards.

The theater in the film is actually the Comédie Française, the theater that has existed since the time of Molière and has the kind of status in France that, say, the most prestigious Shakespearean theater would have in England. If you know Paris well you can tell because the crucial scene takes place in the "colonnade" along the rue de Rivoli - one end of which is at "Palais Royal" (i.e., the Louvre) and the other end of which (which is where the protagonists run to in the culminating chase) is where the theater in question is.