The resistance is already there, it's already happening. Car owners in Paris are furious, and bike infrastructure is already taking away space from roads. High traffic roads in the center have been downright closed and made bike-only.

It is feasible because Paris (the city itself, excluding suburbs) is a very crowded city, where owning a car has always been a luxury. People living in Paris itself who can afford a car, with the associated parking space and everything, are a minority.

People living in the suburbs are more likely to own cars and drive through Paris, but they don't elect the Paris mayor, so their opinion doesn't have much weight.