Advance purchase train tix: FRA to Zermatt, to Chamonix, to Lyon, to Paris, back to FRA.

Hey Team - we're a family of 4 flying in/out of Frankfurt for a 3 week trip to Zermatt, Chamonix, and Paris May 24 - mid June. Looking for the best way to purchase train tickets. Is there some universal pass we can get?

We are comfortable with European train travel, but the destinations don't seem to be as straightforward as we've had in the past.

I'd love to keep the train rides to less than 4 hours each and like the fast trains (TGV), but willing to stop for fun!

-FRA to Zermatt: Maybe stop in Basel to eat? I don't see a faster way than ~7 hrs.
-to Chamonix: ~4 hours? Is there a faster way?
-to Lyon: ~4.5 hours on BlaBlaCar Bus?
-to Paris: TGV - this one seems expensive, cheaper are sold-out (maybe because it's Sunday?) (booked via trainline or SNCF)
-back to FRA: SNCF $66US hrs (booked via DB)

Ideas?