Driving without a French driving license? (Paris)

I’m an American living in Paris- been here for 3.5 years. I just recently started a new job working in the banlieu- there are buses that take me between there and Paris, but I would much prefer to drive to work. My American driving license is actually expired, though even with that I’ve rented cars for occasional trips outside of Paris, and never had a problem. (no one in france ever notices the expriation date listed on the license)

It would cost me hundreds of euros and 3 to 6 months to legally get a French license. I’m considering just getting a car and driving to and from work, then if I do happen to get stopped, giving the officer my american license and acting like a tourist.

I’m wondering- what do people think of this idea?