In the U.S., there are gated communities. Paris has its own versions– these private streets, which abound in the 16th arrondissement. Usually you have to know a code to get in. One of them, the Villa Montmorency in the southern half, Auteuil, even has full-time guards who patrol the streets and monitor the gates. Inside, behind the screen of trees, is one of the very few (or the only?) places in Paris where large private one-family houses exist with gardens and even swimming pools.
As you can imagine, the Villa Montmorency been a favorite of the rich and famous for many years. Céline Dion, Laurent Dassault (airplanes), Wladimir Taittinger (champagne), Arnaud Lagardère (Lagardère Group, a giant international media company that owns, among many others, the Hachette group), Alain Afflelou (glasses), Tarak Ben Ammar (movies), Carla Bruni (Sarkozy's wife), Zlatan Ibrahimovich (soccer), Xavier Niel (internet), Sylvie Vartan (singer famous in the 60s and 70s), Carole Bouquet (movie star), all live there behind the gates, enjoying the privacy. Servants and "personnel" are not allowed to drive on the streets of the Villa; they have to go in the back way, and every dwelling must be at least 150 square meters, with no subletting allowed. It's a "preserve of the rich that makes le tout-Paris daydream."
There never used to be houses for sale there, back when the French economy was booming, but now there are plenty–if you want to pay €8 to €50 million, and are prepared for France's taxes. Apparently, not enough people are. The rich foreigners who might buy in central Paris don't want to live so far away (apparently the only foreigners are "a Chinese and a Russian," Ibrahimovich, plus an Indonesian who bought last year), and the "franco-Français" are leery of the image of a "ghetto for the rich." Possibly another reason is the giant public housing project going up next door, whose inhabitants will be able to see down into it.