"I have found that Burg Eltz is not open til late March."
Marksburg, a never-destroyed Rhine castle in Braubach, is open all year. It's 10 minutes south of Koblenz by train in Germany's Middle Rhine Valley. (Koblenz is also the train hub where you would connect for the Mosel and Burg Eltz.)
http://www.marksburg.de/en/
Fasnacht (German Carnival) takes place at the end of February in Mainz and Cologne (and a few other cities as well) with the Rose Monday parades on Feb 27. Since Braubach lies in between, it might be good to schedule a stay in one city or the other, or nearby. Mainz is a good choice with lots of good sights of its own and with easy access to Frankfurt, Speyer, Ruedesheim, and other destinations.
Trier, Germany's oldest city (ancient Roman outpost, see Rick Steves book) is near the Luxembourg and French borders, only about 3.5 hours from Paris by train. It might be a good starting or ending point for all of the above destinations as you make your way to/from Paris.
Info on Mainz, Speyer, Trier: http://www.en.romantic-cities.com/Cities.5616.0.html