MSN.com has posted an updated article on rules for transiting European airports. There are still major problems for Americans who might want to connect at many European airports.
Amsterdam, Paris (all airports) and Zurich (no mention of Geneva) all are effectively prohibiting US transit passengers with destinations in the Schengen Zone. Amsterdam also blocks those wanting to transit to another EU country.
Many other airports require negative COVID-19 tests. Frankfurt's policy sounds the strictest. The test must have been taken no more than 48 hours before arrival in Frankfurt. My speculation: Based on reports of people's testing experiences, one cannot assume PCR-test results will be available fast enough to meet that requirement. Some other types of tests are acceptable in Frankfurt; some may be faster. However, those other tests might not be acceptable at ones ultimate destination, so some travelers transiting Frankfurt might end up taking two tests.
The information in the article was--one hopes--correct at the time of original publication, but it could change at any time. No one should rely totally on the information in the article, but I think it's a useful first step in learning about the various hurdles one might face in flying to Europe right now.