In Japan, only certain classes we allowed to have weapons. Was there a black market for arms among lower class in Japan? Were there similar laws against peasants owning weapons in Europe?

I'm not sure what era you're going for, so I'll take "peasants" and run with it. ;)

There weren't laws as such against owning weapons in medieval Europe. Cost would have made the purchase of nicer weapons prohibitive for a lot of peasants, certainly. But even the Jews of the 11C Rhineland had access to swords and armor. Skip forward a few centuries, and it was dangerous not to carry a weapon in southern Germany. Not because of bandits, but because everyone carried them--except pacifist Anabaptists. Being an adult male not carrying a weapon got you arrested as a heretic.

Medieval clergy were not supposed to shed blood in violence. But that is a different kind of exception.