and welcome to France!
I do advice you to go the Vosges if you can... The area might not offer spectacular views and sceneries like it would in the Alps or in the Pyrénées, but it's a very nice place to hike.
Here is a link to a photo album of Ultra lighter meetings in the Vosges. http://picasaweb.google.fr/MUL.VOSGES
some others http://www.randonner-leger.org/forum/viewtopic.php?id=6746
You should probably speak french, so you won't have so much troubles to understand the threads..
What is great if you go to the Vosges is that there are numerous very good shelters and refuges that you can use for free. => http://www.cc-vallee-doller.fr/PhotosSousRub/Projets/d%E9pliant.pdf (in the South of the range of mountains) then you won't have any problem to hike there in winter even you're not so well equiped.
Otherwise, you can try Le Jura (http://www.randonner-leger.org/forum/viewtopic.php?id=5025)
nice views on the Alps with clear weather... but not as high. Unfortunately, no cabins there...
I don't know the area around Paris, but I've heard about some nice hiking spots at the forest of Fontainebleau...
Maybe Britanny? as a coastal area... it shouldn't get too cold in winter...
Feel free to visit our national hiking light forum at www.randonner-leger.org, it might give you some ideas ;)
To end this very long post, I really advice you to go to the vosges. It's a really nice place : http://www.randonner-leger.org/forum/viewtopic.php?id=3936 ;)
I know a few guys there really willing to meet some new partners (cf. picassa album), so you can contact without any problem... They might give you other ideas.
Have fun in France!