It only applies to vehicles not owned by Parisians.
It's a start, you have to roll out measures like this slowly or people will oppose it. It's the same with sane tempo restrictions in cities.
The current trends of centralization and control involve restrictions on freedom of movement, making personal cars one of the pressure points. In socialist countries, ordinary citizens take the bus. Rest assured, Macron et al. will continue zooming through Paris boulevards in their armored SUV cavalcade.