Paris - Switzerland : definitely the train. Much better to travel overland at 300 km/h.
Eurail won't be useful for transportation within Paris : RER, métros, buses aren't included. Tickets are cheap anyway and wouldn't be worth using a pass day (if you could use the pass I mean!).
I'd compare both Eurail vs Swiss Half-fare card* + tickets for France and Italy. High-speed train tickets can be very expensive or very cheap... depending on demand.
*The Swiss Travel Pass is expensive and only worth if you cross the country every day which you won't.
Seat reservations cost extra with Eurail, they are required on high-speed trains. Have a look at :
https://www.seat61.com/how-to-use-a-eurail-pass.htm
https://www.seat61.com/interrail-and-eurail-reservations.htm
For example on 25th May you can do :
- TGV Paris Gare de Lyon - Lausanne 07:56 - 11:54 54€ 2nd class / 74€ 1st class (children reduced)
It's not a bad price honestly.
Then get the Swiss Half-fare card (2 x 120 CHF) + free Swiss Family card for the 10 y.o.
You get 50% discount on tickets and the kid travels for free everywhere (including on expensive peaks such as Jungfraujoch).
Already 110 CHF saved with Jungfraujoch!
Millions of Swiss people have that discount card (195 CHF a year for residents) as it is very quickly good value.
You can buy point-to-point tickets as you go -> valid all day on the selected route. Use SBB app or sbb.ch to get an idea. Half-fare is always the first price shown.
For the journey to Italy : Spiez - Milan is the fastest route, no doubts. Due to year long works along the route there is a closure in Stresa every weekday from 10am to 3pm -> meaning you have to take the 08:05 or the 14:05 train.
To save money do like most Swiss do :
- board the EC in Spiez and stay onboard until Milan
- 26.50 CHF point-to-point one-way ticket until Domodossola, the border point (Swiss Family card valid)
- Domodossola - Milan - Florence through trenitalia.com
Questions welcome.
Domodossola - Milan is very cheap on your date, "family offer" = 25€ altogether.
On the other hand the 11:10 train from Milan to Florence is really expensive and I don't really know why... it looks quite empty right now. If you don't want to pay so much, stop for an hour or two in Milan : all other trains are half the price.
Hope I didn't give too much info! Read bit by bit :)
Thank you. This is very helpful.