Why do French authorities put up with this ?
They probably want to "keep the peace"? With 20% of their yoot population, um, "immigrant" (and growing) and 15-18% of their military "immigrant" (and growing), the French have themselves a king-sized problem larger than the torching of a few hundred, or thousand, or million, cars.
In case this isn't a rhetorical question(!), it's partly because they're afraid of the 30 million unassimilated, violent, and anti-western Muslims in their country. In a jaw-dropping refusal to consider the history of tyrants in Europe, they insist on believing that appeasement will make the Islamofascists calm down and go home.
It's also, according to Mark Steyn, because of the stubborn adherence of the political class to the vision of a pan-continental Eutopia that was supposed to insure that Europe would never again succumb to militant nationalism, like Naziism. That post-national world view has simultaneously made them unwilling to defend their own country, and blinded them to the rising threat of Islamofascism.