Montpellier is very cosmopolitan for a city of its size and has a wide variety of ethnic cuisines available, in addition to traditional French food. The centre features a plethora of over-the-counter sandwich shops and similar places specializing in kebabs nearly as many of these as there are hair salons and real estate agencies. If you're looking for the classic French cafe experience, try any one of the many bistros near La Place de la Comedie. For a good coffee in a more relaxed atmosphere, there's also a nice cafe near the Louis Blanc tramway stop.
Montpellier is dotted with eateries ranging from very touristy to truly authentic. Geography plays a large role here: the matrix of restaurants in the town square generally cater to visitors who are optimizing for convenience, but not for price or quality so much. Head away from the city center--north, south, west, but generally not east--for a more genuine experience.
