I lived in Paris for three years, and I did a lot of street photography -- never had a problem. Do watch out for scam artists who will try to take advantage of your presumed greed: you'll see someone walking toward you suddenly bend to the ground and come up holding a gold ring in their hand. They'll ask you if it is yours, or what they should do with it, the whole idea being that somehow they are "willing" to give you the seemingly expensive gold ring for a relatively small sum of money. Of course, the ring is fake, the scam artist palmed the ring that was never on the ground, etc. I used to just keep walking right past them.
Yep, gat caught with that one. Near the Eiffel Tower. Was a bit nonplussed when we offered a modest reward to be abused that "she couldn't even buy a Coke with that!".