Hi and welcome to the forum (and to the Orsay area - I'm located not too far from there).

You're going to do better by living out in the Orsay area. It's a little less expensive than Paris, and you save yourself about 30 - 40 minutes each way on the RER B line. (Plus, the B line has a bad reputation for being the one most often out on strike.) There is an association in the area known as "Science Accueil" which can help you find lodging and stuff to do - they target students and researchers in the area and should be contactable through the university or on their website: Science Accueil - Accueil.

To position yourself nominally closer to Paris, you may want to try to find a place to live in Palaiseau or Massy, but the area around Orsay (Bures or Gometz) seems pretty popular for those at the university.

You're getting paid as a PhD candidate? Not sure how that works, but it's not quite tax free in any event. You will have to file a tax return, but chances are you won't owe much (if any) income tax on the income unless you're incredibly well paid for a student/researcher. Science Accueil can probably provide more information on this, plus some assistance if you need it.
Cheers,
Bev