Yes, this is possible, but it is VERY, VERY expensive - you have been warned!!
Here are some websites that will help you though, should you decide to go for it:
DB Autozug - Motorail Information
France Motorail (Raileurope)
Have you considerd getting your Lady to fly down to the South of France (there are some VERY cheap flights like Ryanair & Easyjet etc) You RIDE down and back, and join up with her in the south?? - you might find this is much cheaper than the train, and will give YOU a chance to have some solo 'blats'!!
ALSO if you perhaps stay in ONE place, (or perhaps limit to TWO different places) and book a hotel with jacuzzi or pool, for example, then ride out each day, that would give her a chance to relax her back & recover during the evenings.
This might not be as much touring as you want to do, but could be a good compromise for both of you, under the circumstances!!