Europe for 18 days

Umm, you’re doing way too much. Sleeping on the trains is terrible and doesn’t save you time when you’re exhausted the next day. Fly the longer legs and cut back. You will learn, grasshopper.

If you want to go to Switzerland drop Nice. it is out of the way. Train or Fly to Basel or Zurich and take the train to Luzern or Lauterbrunnen. Stay there Then take the train to Turin then to Venice and cut out Rome.

You can take the 7:23 a.m. 4-hour TGV train from Paris-Gare de Lyon to Zürich HB (main station) arriving at 11:26 a.m. Then you can take a train leaving track 4 (every hour at :04 after the hour) to Luzern. Then take the very scenic 2 hours and 20 minutes train ride from Luzern (leaving every hour at :05 after each hour) traveling past mountain lakes and waterfalls to Lauterbrunnen VIA BRUNIG. Lauterbrunnen is in a valley in the heart of the most spectacular part of the alps, near the Jungfrau. Allow a few days to enjoy that area to make sure you'll have good weather for the best views.

Then from Lauterbrunnen, leaving at 7:03 a.m., you can train to Venice (Venezia S. Lucia) via Spiez, changing trains in Milan, to pull up in the heart of Venice at 2:10 p.m.

You can get details from the Swiss transportation app:
www.sbb.ch/en

It is a lot and I think something must go, but first, please tell us, when are you traveling? Seasons make a difference. Did you already purchase tickets into Paris and out of Rome?

(The cars at the Torino museum are fabulous and it is a lovely city!)

Jordan, night trains are no longer common. They have been put out of action by High Speed trains for medium distances and cut-price airlines for longer distances.
With 16-days I think you need 4 places. How about: Paris - Switzerland - Venice - Rome. All these legs are suitable for (fast) day trains.

LindaL's comment: "You can take the 7:23 a.m. 4-hour TGV train from Paris-Gare de Lyon to Zürich HB (main station) . . . .. Then you can take a train . . . . to Lauterbrunnen ." is incorrect. That would be doubling back on yourself.
Her recomendation of the Lauterbrunnen Valley is good.
Get off the train from Paris at Basel, and take a train from their direct to Lauterbrunnen (or wherever). You save hours that way.
You can visit Luzern (and go over the lovely Brünig Pass route) as a day trip from Lauterbrunnen
See Swiss rail map here: https://www.sbb.ch/content/dam/sbb/de/pdf/freizeit-ferien/ferien-kurztrips-schweiz/internationale-gaeste/uebersichtskarte_synoptic_map_2017_low.pdf

ChrisF's route from Basel could save you about 2 1/2 hours on the train, by my calculation (5 1/2 hours from Paris vs. 8 hours). However, that faster, more direct route from Basel goes through industrial areas, especially north and south of Bern. As I recall, the gorgeous scenery mainly reveals itself south of there, as soon as you've passed Thun, and all the way to Lauterbrunnen and the Jungfrau region. I was routing you on a longer, less direct, but, in my opinion, more scenic route, which was not industrial. However, if you took the 7:23 a.m. TGV train from Paris, my route wouldn't get you to Lauterbrunnen until 3:25 p.m. ChrisF's route could get you there at 12:55 p.m. giving you that afternoon to start exploring the area.

And I'm with ChrisF's suggestion of limiting your destinations to Paris, Switzerland, Venice, and Rome, so you'll have enough time to easily get there and see each place.

Jordan - Would like to know what you are thinking. Any reactions?