We will be transiting through Frankfurt, with about 2 hours between our flights. We are US citizens that are fully vaccinated. The destination country doesn't require any testing for us. Would Frankfurt authorities need to see a test for fully vaccinated US citizens?

You can look up this information yourself on the Traveldocs website. It’s similar to TIMATIC but more helpful to the general public as TIMATIC is limited to travel professionals or sometimes you get access via a link on an airline website to very restricted info.

https://www.traveldoc.aero/

As you are in transit, not leaving FRA airport, not entering Germany, you are exempt. However I never leave home without my proof of vaccination.

Considering the steep increase in cases of Covid among the fully-vaccinated, I wouldn't be at all surprised if testing requirements also increase during the summer travel season. But as you're just connecting at FRA and the destination country doesn't currently require a negative test, you're probably ok. Just keep an eye on the rules as they can change at any time.