There are several reports here that the various French highways are run by multiple different companies, so you card can work in one toll booth and not another. This includes reports from people who have a true chip and PIN card issued in the US. So, you can never count on your card working in a French toll booth.
There are also reports that the French EZ Pass devices are not easy to get for short term visitors.
Just go to an ATM before your drives, so you're prepared.
EDIT: no, the rental car company does not bill you. You have to pay the tolls at the time you use the roads. And as Sam said, for Switzerland you have to have the vignette (pronounced veen-YETT-uh) before you use any Swiss highways, or you'll get fined.
You also need an International Driver's Permit to drive in France. You get it a AAA (if you live in the US), even if you're not a member. It's good for a year, but you can start that year on any date. You carry it with your US license; it does not substitute for it.