There is great rail service throughout/between France, Switzerland, and Italy. You can buy in country passes for Switzerland and France. I'm sure you can for Italy as well, but I have no direct experience.
Between Paris/Switzerland/Italy:
List of TGV services - Wikipedia
TGV is likely your best option here. It's a French (SNCF) governed high-speed rail line centered in Paris. It will get you around France and to a number of neighboring countries included UK, Luxembourg, Germany, Belgium, Italy, and Switzerland.
Inside Switzerland:
Buy travelcards and tickets online | SBB
Switzerland's national rail service is SBB. You can purchase up to 15 Day travel passes which get you access to most regional and national travel services including rail, boat, and bus. Not sure of your budget but Swiss carriages are decent quality (especially IR) so 2nd class is fine, but book 1st if you can afford it. I would purchase online and download the SBB app.
Inside Paris/France:
You can purchase something similar to a Swiss travel pass to get around the RER/Metro, though you'll have to purchase in person at a metro station (or at least I did). If you're arriving by train, you should hit a hub station like
Gare du Nord or
Gare du Lyon. You basically print off a little card and have access to every most regional/national lines for 1/3/5 days or whatever.
Not up on rail service inside of London or Italy.