Germany, France, and Switzerland in May

Three countries sound a lot without context but the travel distances of the destinations are close to each other. Therefore I think that your planned total travel duration seems suitable for the destination list.

I hope you are aware that all three countries have multiple cultures and layers, so if you visit one or two destinations of each listed country you likely did not visit a representative place for the whole country.

For train journey planning in / from / to Germany use https://int.bahn.de/en.

Have a nice journey.

While I like Basel very much and love the Zürich small gardens in the banking district, I have been to Switzerland many times and my visits to both of those cities have been quite small parts of my Swiss visits.

Do you not have any interest in viewing or visiting the things that Switzerland is most famous for - the Alps? Both Zürich and Basel are in the lowlands, hours away from the famous Alps....

My travel companions are worried this isn't enough time to visit all three countries...

I think that sounds like a very nice time.

Staying with friends in Frankfurt is a nice way to see Frankfurt but I wouldn't call it seeing the country. Hopefully that's a short stay. South of Frankfurt there are lots of nice places in Germany to visit, places not far at all from Strasbourg and Basel that will add some local flavor to your time in Germany:

Gengenbach, old walled town with towers and cobblestoned streets
Tübingen
Freiburg
The Black Forest region and its old-world villages

It is not possible to stay in Frankfurt and visit these places on day trips - but you could perhaps stay in Freiburg or Gengenbach and do outings to Strasbourg, Basel and some of these other destinations. Train transport around the Black Forest can be a scenic way to get around - and the trains are free of charge when you stay in certain Black Forest towns:

https://www.youtube.com/watch?v=KkgzMXQ7blQ

If you are just staying in the 4 cities, you won’t be rushed. Depending on any day trips you may gake, you may fond the train travel a bit wearing. I don’t and enjoy relaxing n the train going back to my base.

Russ mentions Gengenbach and Tuebingen, two worthwhile towns to visit. Gengenbach and other towns along the Kinzig River are convenient to visit from Strasbourg. Yesterday I made feservations for Gengenbach next fall, my fourth visit.

Russ had some excellent suggestions.

Not sure why you focused on Basel and Zurich in Switzerland, those are OK, Basel being better than Zurich, but there are BETTER places to take visit.
Lucerne is wonderful, also consider Interlaken.
https://www.myswitzerland.com/en-us/destinations/interlaken/

Between Frankfurt and Switzerland you could visit Heidelberg, Wiesbaden and Mainz.

Are you going to fly in and out of Frankfurt, or is one end of the trip at a different airport, e.g. Zurich?

Anyway, your plan sounds reasonably paced. Frankfurt-Strasbourg-Switzerland should all be doable comfortably in an arbitrary morning.

In or around the Switzerland part, I would recommend either the alps or lake Constance, depending on your personal preferences.