Another option...
Firenze - Milano - Luzern (possibly Arth Goldau - Luzern) - narrow gauge Golden Pass route on the ZentralBahn rack (cogwheel) railway via Brunig Pass and Meiringen (of Sherlock Holmes Reichenbach Falls fame) to Brienz and Interlaken Ost.
I did the Luzern - Interlaken bit (and up the hill) as a day trip with my wife the first time she went to Switzerland many years ago, long before I knew from this website I shouldn't go in May. It was either the second or third week of May, and winter had hung on a bit that year. I just thought the extra farmyard smell was how Swiss farms smelled, having grown up near and next to farms in England. (It is sprayed manure, allowed to ferment all winter, to bring up the grass quickly after the thaw). My wife had the thrill of seeing snow in the trees of the higher bits of the ride, and we picked up snow on the platform when we hopped off - and straight back on - at one of the stations along the way.
The Monch, Eiger and Jungfrau were at their best that day looking over from the cliff edge at Mürren and seeing them for (her) the first time was breathtaking.
No matter how much is shut down between seasons something is always open. If that's when you can go, then that's when you can go. You might get rubbish weather though..... or nice.
Then either backtrack to Luzern, or much simpler if you broke your journey in the Berner Oberland, Lauterbrunnen, Mürren or Interlaken, continue via Interlaken West and Bern to Basel, where I suggest you make your second break of journey. All seasons of the year Basel has plenty to interest and plenty to see. There is an Ibis right next to the station and a Great Western across the street from the main entrance, and hotels in Basel give you free city transportation for the duration of your stay.
Then a very simple, short, and fast run from Basel to Paris on a TGV.
That's what I'd do, anyway.