Yeah, that's in short Paris' problem. The last few mayor all wanted to remove all cars from Paris, but they all failed to provide alternatives and failed to meaningfully improve public transportation, especially since most of the network is overworked.

Also most of the cars clogging the roads are going from one suburb to the other and the way the road network is built makes that going through Paris is the best (sometime only) way to go from one side of Paris to the other.

Edit: Not all cars are banned, half of them, based on Vehicle registration plate (even or odd number).

> The ban bit is easy

The ban was made in response to the current pollution problem, but removing half of the cars has a pretty weak impact on air poltution.