I'm not sure Paris has one of the best public transit in the world or maybe that's just an indicative of the sorry state of public transit worldwide. I mean I wouldn't call world-class a system where just a single failure easily strands 1 million people halfway to their destination and where trains are delayed and cancelled routinely, often without information given to passengers.

I'm in favor of more public transportation, but if you think people use car willingly in and around Paris, I don't think you've tried it; it's so bad that only people with no viable choice will use a car. Or maybe you could explain (for example) how my sister in law was supposed to carry her two baby kids to the daycare using an overcrowded metro (and bonus, through stations without working elevators) or how my brother was supposed to carry the equipment he was using to constructions sites he was working. And then you've got all the places where taking a car is a 30 min trip vs 2 hours by bus or public transportation (thankfully the Grand Paris initiatives are helping a lot there).

For now, removing cars in Paris just push them around the city, because the public transportation network isn't ready.