Nicole,
When are you planning to take the trip to Europe? If you have time, I would HIGHLY recommend pre-reading the Guidebook "Europe Through The Back Door", as it will help you a lot with the "differences" you'll encounter there. Read the "Rail Skills" section carefully!
With only two weeks and the fact that you have return tickets from Frankfurt, careful planning will be essential to minimize travel times between locations. Using budget airlines in Europe is a good method, but booking LONG in advance provides the best prices. One point to note is that European airlines allow ONE carry-on bag ONLY.
A few choices to consider. You could fly direct from Frankfurt to Rome, however it appears that Air Berlin is the only carrier on that route (unless you can book a connecting flight with whichever airline you're flying on). Air Berlin flights depart at 17:25, layover in Vienna and arrive in Rome at 21:05. That's NOT something I'd want to do after a long trans-Atlantic flight!
Another option would be to go to Munich by train to begin with (there's a station right in Frankfurt Airport) and spend a few days getting over jet lag. From there travel by TGV to Paris (there's a direct train departing at 06:20, arriving at 12:34 - reservations compulsory). The TGV travels at 300 kMH, so it's a fairly quick trip, despite the distance.
Given the distances between the areas you want to visit and the short time frame, it's going to be challenging to work out the transportation links. You might consider visiting areas that are somewhat closer on this trip.
Check your local Bookstores for the France or Italy Guidebooks, as they have great suggestions for budget Hotels in each of the places you want to visit, along with transportation and sight seeing details.
Good luck!