Documents necessary (and recommended) for first time travel to EU for US Citizen

In general US Citizens are given very free entry to France and other Schengen countries. As you've discovered, no visa is required, and generally there is little to no details requested at the border.

Most of my entries into France consists of something like me saying "Hello" and handing over my passport, the immigration official maybe giving a grunt in response to my greeting, looking at my passport, stamping it, and giving it back to me. (I'm Australia, but the process is basically the same for US citizens).

However technically there are a few things she is required to have. Ideally she will have a return ticket. Technically this isn't a requirement, but the policy is that "Visitors not holding return/onward tickets could be refused entry", and this would be especially true if she stated that she's coming to visit her fiance on the grounds that they may think that she's likely to overstay.

She will also technically need to hold sufficient funds for her stay. It's unlikely that they would ask for this information unless it was asked, but having a copy of your bank statements with her certainly wouldn't hurt, even thought it's unlikely it would be required. The fact she's staying with you will also reduce the required funds due to the lack of need for a hotel.

As far as health insurance, it's not required - but it's always a good idea. Presuming she has health insurance in the US this probably covers her in Europe, but you'd need to check the policy to be sure.

As with all border crossings, there's no way that anyone can ever say exactly what happens. If the border officials believe that she's planning to live in the US, or doing anything else outside of what is allowed under the 90-day visa free period then they always have the ability to refuse her entry and send her back to the US on the next plane - but the odds of that happening are extremely small.

As always, the best plan is to offer no information unless asked. Be pleasant without going overboard. And answer all questions truthfully if/when asked, again without giving much more information than is required. Odds are they'll presume she's just yet another American tourist come to visit the Louvre and La Tour Eiffel, and let her on her way with little more than a grunt.