Most of the non white Europeans in Paris are from either French North Africa (Algeria, Morocco etc) or from French Central Africa that would have come over on a similar system to many of the Caribbean and Indian populations in the UK.
There's a huge problem across the whole of France right now with Roma gypsy pickpocket gangs, who as EU citizens cannot be stopped from operating there. Recently staff at the famous Louvre museum threatened to go on strike unless they received protection from the pick-pockets.