I live in France, about 150km north of Limoges. Our two local towns had small (20 in one and 40 or so in the other) demonstrations by students from the Lycee about school conditions, lack of teachers that sort of thing. They had placards, they shouted a bit and some parents marched with them.
On the Sunday I was at a village fête, where the noisiest things were the folk dancers and the only things that got roasted were the chestnuts!
No violence, no looting, just taking part in a democratic demonstration.
Protesting on the streets is pretty normal here- it can be a bit inconvenient (like when the local farmers left a huge pile of manure outside the Préfecture) but not violent or lawless.
What was seen all over the media were peaceful normal protests taken over by thugs with their own agendas- either political trying to stir up trouble, or simply to loot and smash things “for fun”.
Overwhelming people are shocked and horrified by events- our local and other town halls including Limoges have had peaceful crowds gather in solidarity against the violence.
I see a man has been arrested in Limoges- good! Whether these events have been instigated by the far left, the right, foreign governments, immigrants or just random thugs or a mixture of all of these depends on which paper you read imho.