500 000 is the official number, that is always overrated, just as the organisers number is overrated (800 000 to over a million). Peaceful protesters, int the vast majority of cases and of the cities. I live in a rather quiet and mostly unknown region of France, there have been protests all around, some rioting in the only relatively big city (Saint-Etienne, where two youths have lost respectively an eye and a hand due to a stun grenade thrown by the police), but not in any of the smaller towns.
The apparition of ultra left and right (don't conveniently forget the right, please) groups, and not an islamist in sight, ready and willing to make sure things would turn sour, and followed by looters, is no surprise in the (parts of) cities where media coverage ensures the world will see France all ablaze.
The bona fide protesters know it, the authorities know it, but as usual the latter refuse to cooperate with the former in order to minimise the damages (times and itineraries, coordination with the police, sharing of informations about the violent groups, etc).
Le Monde EDITORIAL
Now of course, everybody and their cousins are blaming only the (far) left, try to insert immigration and islam into the picture, and gleefully announce that France is finished, etc.