Emily,
I'd also suggest using Vueling rather than RyanAir for your flight, even if the cost is slightly higher. You'll have a much easier time getting to and from CDG and FCO airports.
To reach CDG from Paris, you could either ask your Hotel to book a Shuttle (arrange this a few days before you'll be leaving) or take the RER. To reach Roma Termini from FCO, use the Leonardo Express train which is an easy ~30 minute trip and no worries about traffic (buy tickets at the station when you arrive - don't forget to validate in the yellow machine). From Termini it's not hard to access any location in Rome via Metro, Taxi, or Bus (Taxi's are in the front - with your back to the tracks, walk straight ahead).
Which areas of Paris and Rome will you be staying in?
One very important note is that the budget airlines all have extremely restrictive baggage limits. On Vueling I believe you're allowed one bag of 20 kG (at a cost of Eu$10) and one carry-on. If you're over that limit, you'll pay!
Given the distance, I'd suggest budget flight over a night train, especially if time is a factor. The travel time via train will be a minimum of ~11H47M, via TGV & EuroStar Italia, with one change in Milano (that's a day train, departing Paris Lyon at 07:42).
As this is your first trip to Europe, I'd highly recommend reading Europe Through The Back Door before you go, as it covers a lot of details on smart travelling in Europe.
Happy travels!