You can try a part of the pre alps trail "le chemin du soleil"
http://grande-traversee-alpes.com/chemins-du-soleil or la Grande Traversé du Vercors
In France you have two national associations which had built nationals trails FFC (competition) and FFCT (Tourist) . "Grande Traverée" (long cross ) is a trade mark of FFC, for instance GTJ (Grande Travesée du Jura) or GTMC (Grande Traversée du Massif Central) . So FFCT should use others words, for instance TMV Traversée du Massif des Vosges.
Link to the web site of FFC where you can search for "Grandes Traversées"
http://www.ffc.fr/a_VTT/a_SitesVTT/index.aspIn my opinion the best periods are may-june and september