To work it out a little:
The quickest daytime train is
Roma Termini depart 06:00 highest speed train to Torino Porta Nuova
with only one intermediate stop (stay on the train) at Milano Centrale after 3 hours
Get off just before the end at Torino Porta Susa arriving at 09:54
Transfer time 17 minutes
Leave Torino Porta Susa station (change trains) at 10:11 on a high speed TGV 9244
the train will stop at (stay on):
Oulx-Cesana-Claviere-Sestriere dep 11:13
Bardonecchia dep 11:23
Modane dep 11:52
Chambery-Challes-E dep 12:56
Aix-les-Bains-le-Revard dep 13:13
Bourg-en-Bresse dep 14:15
Mâcon-Loché TGV dep 14:36
and will arrive at
Paris Gare de Lyon in the centre of Paris at 16:11.
Total travel time because you are city centre is 10 hours and 11 minutes (the length of the train ride), and there are no luggage issues if you can carry your own luggage (if you are on Rick Steves' tours you will be able to). Take all the food you want and all the drink too, as long as you can carry it and not become a nuisance (if you are doing RS tours, you won't become a nuisance).
Flying - Figure an hour to get to FCO because although the train is faster than that you need to make sure you don't miss one so leave a little fudge time, then 2 hours to go through check-in and security. 2:10 minutes flight time if departure is prompt and no delays on route or landing. Around an hour to get out of the airport or so, and then around an hour into Paris by taxi or RER.
So total travel time flying somewhere around 7 hours and 10 minutes.
Flying is then somewhere around 3 hours faster. Stress, security theatre, scenery, and seat comfort aren't included in the calculation.
As for price, if you get them far ahead they may be about a wash, with the headline price of flying on a discount airline possibly cheaper until you add seat selection, luggage, and the myriad of other charges in.
There is a Night Train option with one change at Milano Centrale at around 11pm,
Roma Termini dep 20:00 FR 9660 Frecciarossa Direction: Milano Centrale
Milano Centrale arr 22:55
transfer time 18 min.
Milano Centrale dep 23:13 EN 220 EuroNight Direction: Paris Gare de Lyon
Sleeper and couchette train , Global price , Couchettes , Bordrestaurant
+ 1 Day
Paris Gare de Lyon arr 09:55
or getting in over an hour earlier if you both change at both Milano Centrale onto that same night train and change again in Dijon at 6:45 onto a fast TGV, arriving Gare de Lyon at 8:37am.
Roma Termini dep 20:00 FR 9660 Frecciarossa Direction: Milano Centrale
Global price , Bar , space for wheelchairs
Milano Centrale arr 22:55
Transfer time 18 min.
Milano Centrale dep 23:13 EN 220 EuroNight Direction: Paris Gare de Lyon
Sleeper and couchette train , Global price , Couchettes , Bordrestaurant
+ 1 Day
Dijon Ville arr 06:43
Transfer time 17 min.
Dijon Ville dep 07:00 TGV 6700 TGV Duplex Direction: Paris Gare de Lyon
Subject to compulsory reservation , Global price , Bar , space for wheelchairs
Paris Gare de Lyon arr 08:37