Yes, but they mostly live in the suburbs of cities like Paris, while the inner city remains affluent and white. Do Europeans just do a more effective job of keeping poor people and ethnic minorities from moving into the inner cities in the first place?

A lot of continental inner-cities (Paris, most Italian towns) were already too expensive way before "immigration waves" were even possible. In that sense, newcomers never got a chance. Any town that has existed since Roman times has had two thousand years in which to solidify the link between location and social status, to a point that will likely survive anything bar catastrophic events.

The suburbs didn't exist when people started immigrating to cities like Detroit.