Doing some very general googling, I found a couple of basic Q&A sites that refer to the fact that extra drivers in Europe nearly always generate a fee, whereas in the U.S., the "free spouse" thing is more common.

Not that these sites are necessarily accurate - for example, one site says that National and Hertz charge extra for spouses in the U.S., which isn't true so long as you're willing to give them enough personal data to become a member of their respective frequent-renter club.

But looking at the fine print for all of Avis, National, and Hertz...the words "U.S. and Canada" are always in there somewhere.

It sounds like you'll have to pay the 37 euros if she really needs to drive.