Riots happen mostly (and i would say only) in the suburbs of large cities, kind of our ghettos. Typically after some sort of incident with the police (I'm not saying the cops are at fault necessarily but the relationship between the Police and the population in those neighborhood are strained to say the least).
I think I've never seen one real riot in Paris in 40 years here. On the other hand, and it's a cultural thing here, there's tons of protests, gatherings, etc....
Most of them are peaceful. But when there's students involved or trade-union, you have generally a bunch of either ghetto kids who joined to pillage stores or left/right wing extremists who will infiltrate and destroy property. That's it.