Brooklyn and Queens; formerly "affordable" places to live in New York, are now getting $4,000 (or more)/mo for 1-bedroom cribs. I've seen it with my own eyes, in Manhattan. Areas like Alphabet City, that used to be considered "dangerous," are now primo real estate, and well-dressed young couples walk their toy poodles around these neighborhoods.
It's only a matter of time, before NYC becomes an East Coast San Francisco. Manhattan is pretty much there.
I am not personally familiar with the way France is structured, but I have been told that the cities are where the wealthy live, and the suburbs are where the not-wealthy live.
From what I have seen, Seattle is becoming that way. I was pretty surprised, when I visited some friends, down in the suburbs south of Seattle, and saw that it was actually a rather scruffy area. I had gotten used to Bellevue and Redmond.