I remember listening to an EconTalk podcast about when this was tried somewhere in Latin America. There was a bustling trade in fake license plates so you could swap them out and the number of cars people owned spiked up. In the end it was not very effective.
Obviously,the Paris experiment might have a different outcome but I suspect the Parisians will find ways to drive on the prohibited days. Uber/Lyft/Sidecar have to be giggling in glee. (I can't remember, did Paris ban ride sharing?)