Update: Charlie, here. In Charlie's world, insurgencies are violent political campaigns for the purpose of establishing governance of some (portion of) territory, typically characterized by indirect confrontation with government troops and a parallel political organization. Said differently, you would need to answer yes to each of the following questions:
- Are the actors organized?
- Is that organization interested in eventual governance?
- Does that organization have a non-violent, political element?
- Is the violence characterized by guerrilla tactics and avoidance of direct confrontation?
For her money, Paris is experiencing riots (no organization, no interest in governance). There's little chance they could develop into insurgency. It might possible, however, for the rioters to somehow come together over time and engage in something like resistance warfare, which is mostly interested in punishment and disruption instead of actual governance. In a more or less functioning democracy like France it would be difficult for such a group to operate in the open for long, meaning that over time it would probably morph into a clandestine "terrorist" group. Again, not likely, but not outside the realm of possibility.
Update II: Jaysus! And it's controversial to call the rioters criminal? They're shooting at the police with shotguns! And check the block on Charlie's fourth characteristic...