Questions like this are often put here-also for EUR students doing a yr in a foreign country and the exact answer is :Blurry. There are no really set rules for that. In the past this was far more imprt-as InterRail-for EUR people and those who could prove to stay there- was FAR cheaper as EUrail-which was also only for 1st cl for those a little older as junior.

But all that has gone. YOur daughter can simply use her US-passpt in the rare cases it will even be asked for and hence use EUrail. She likely has a residence permit, as FR is one of the utter most burocratic countries in EUR, but that is separate from that. Only in case of a very smart and inquisitive inspector (some countries do have special anti-fraud squads appearing in very rare cases) who also checks the passpt and then sees she has arrived much earlier as a normal tourist, there may be hickups. Dont fret-minimal chance. The big advantage of EUrail compared to Inter is that it has no limits on how often one can also use it in country of actual residence-as that is out of EUR!

And I guess you have noted it-current vendredi-noir (your daughter will know the translation) now for a few days-20% off fro some types of pass.

Also bonne chance for the needed RES in pesky SNCF-TGV-but again daughter lives there and can try out the SNCF machines ´grandes lignes´ and improve her knowledge further!

Thank you for your help.  What you said makes sense.  I will ask my daughter about what the stamp on her passport says exactly.  I am always one to take a small risk, but my concern is that if an inspector calls attention to it, it could cause a problem with my daughter’s employer. Thank you again.

I don't see what a potential effect a very, very unlikely thorough ticket check will have on your daughter's employer... She can prove she's not a European citizen, so she's entitled to a Eurail pass. No discussion about that. 

Even in the again very, extremely unlikely event she gets fined on public transport, her employer won't care or even need to know those stuff... It's just a ticket mistake, not a criminal offence. No need to worry.

You should by a Eurail pass, so then she can use it to get around in France relatively cheaply too, without being limited to a trip day to get out or of France (the only difference with Interrail, it's forbidden to use it in your home country) . 

Absolutely no problem with train inspectors - they have no interest in domestic matters, only that passengers have a valid travel document (and reservation where these are required). If they do want confirmation that you are valid Eurail pass users your daughter’s passport will satisfy them, as would yours of course.