"Russ - that sounds like a good idea. Any reason you suggested Mainz?"
Mainz is almost as close to FRA as megacity Frankfurt itself - about 20 min. And you can take a direct train from Mainz to Mannheim.
The old town part of Mainz near the Dom (cathedral) and Marktplatz (market square) and along Augustinerstrasse has been given over to pedestrians. It's a great place to stroll around, have a bite to eat, maybe outdoors on the market square, shop, kill some time. Some museums and churches there too.
Mainz old town 1
Mainz' large Marktplatz
The Ibis is a good budget choice near the old town. The Hilton Mainz is near the old town as well and on the Rhine. There are also several hotels near the main Mainz train station that will do the job, though overall this area lacks atmosphere and is a good bit further on foot from the old town via some heavily trafficked streets. If you stay at the Ibis, you can easily use the auxiliary MRT station, only a block away, to travel south to Mannheim by regional train - or get on there to reach Mainz' main station (only a few minutes) to connect with a high speed train to Mannheim and on to Paris (the route you likely would have traveled from FRA.)
But it might be more interesting for you to travel from Mainz via the Middle Rhine Valley instead. Mainz-Cologne offers some of the best train scenery in Europe. Change in Cologne for Paris Nord.
Oberwesel on the Rhine
Trains hug the river