I will be flying from Paris to Munich, then from Munich to Rome. I really only need a small portion of my luggage while in Munich so it would be oh-so convenient to send my luggage via train (or whatever) from Paris to Rome where I would claim it upon arrival. Is there such a service?
The general rule is that you are expected to fly with your luggage otherwise it is considered to be a cargo situation (and may not be cheap vs. the inconvenience).
I would suggest to first check with the airline you have tickets with.
most airlines for international travel require a positive bag match, meaning if your bag is on the aircraft you must be on it too. They also restrict cargo shipments to "known shippers". You would have had to establish a shipping relationship with that carrier. You might want to contact UPS or Fed Ex, I know that in the US they will ship luggage.
Hope this helps