"I am really confused with the train service in Europe."
The best way to find train schedules is on the Bahn (German rail) website, which has schedules for almost all trains in Europe and is easy to use. Here is the site: http://reiseauskunft.bahn.de/bin/query.exe/en
and here is Rick's tutorial on how to use it: http://www.ricksteves.com/travel-tips/transportation/trains/online-schedules.
This site will only have prices for trains that start or end in Germany. To look at prices for other trains, and to confirm schedules, you look at the site of the country where the train starts. In this case, that's France, so use SNCF: http://en.voyages-sncf.com/en/. Choose France as your ticket collection country, to avoid being re-directed to Rail Europe. Rail Europe is a reseller which does not list all trains, and which marks up tickets it does sell.
However, if you actually want to book a ticket, SNCF only sometimes works with US credit cards. You can use Capitaine Train instead: https://www.capitainetrain.com/en. This site matches SNCF's prices (for now, anyway) and is easier to buy from.
Any other train questions? The single best online resource is The Man In Seat 61. For instance, here's his Italy page; you can just use his London to Rome directions and skip the London to Paris part: http://seat61.com/Italy.htm
All that said, Laura is right - for this route, flying is cheaper and easier.