The first through seventh arrondissements, along with heavily congested tourist areas like the Champs Élysées and Eiffel Tower, will participate in the experiment, and several cities around the world, including Montreal and Mexico City, have plans to follow suit. It would be cool if New York City attempted a similar effort, but here's the problem: no one even drives in New York. There's too much traffic.
At any rate, If you happen to be in Paris at the end of September, and suspect an automotive apocalypse, don't be alarmed: all the cars are gone for a (symbolic) reason, so enjoy the peace and quiet while you explore Paris by foot or bike. Hopefully, they never come back.