The Great Crossing of the Ariège, La Grande Traversée de l'Ariège, is one of the best of the seven "Great Crossings" by mountain bike in France. It traverses a section of the foothills of the Western Pyrenees to the south of Toulouse. The Ariège region is rich in history and very scenic.
The route is about 300km long, takes about eight days and follows everything from sealed roads to rough and rocky singletrack with everything in between including mule tracks, walking trails, four wheel drive tracks, and wide flat rail trails. Expect everything from bitumen to mud or rock gardens; from flat to very steep. At times it's challenging; you need advanced riding skills to enjoy this ride.
You can do it as a supported ride using companies such as La Rébenne, http://www.larebenne.com/vtt-pyrenees/index.html or you can organise you own expedition.
The best place to base yourself for the expedition is Toulouse, a great city in itself. There is plenty of accommodation, such as la Petite Auberge de Saint-Sernin, http://lapetiteaubergedesaintsernin.com where you can store your surplus gear till you return since you'll want to travel light. You can hire bikes at places such as Recycles, www.recycles.fr/location-velo-canal-midi-conseils-pxl-19.html. From Toulouse it's convenient to catch the train to the start of the trail at Ax les Thermes and get back to from the end of the trail.
If you can read French there is an excellent guide with maps and all kinds of useful information about logistics, bike shops, accommodation and so on. It's called "la Grande traversée Ariège-Pyrénées" and you can get it here: http://www.chamina.com/produit/grande-traversee-ariege-pyrenees-136. There is a photo from one of its pages in the gallery.
There are plenty of places to stay along the way. Don't bring a tent and camping gear - you need to travel light to be able to enjoy the toughest parts of these trails. There are also lots of signs to show you the way but every now and then they'll just not be there when you really need them so don't go without a GPS trace of the trail in your smart phone or GPS. You can get the trace of the trail here: http://www.vttour.fr/topos/grande-traversee-de-l-ariege,2429.html.
The Great Crossing of the Ariège is a ride you won't forget. It's not that every metre is memorable and you may even get bored from time to time but overall it's a great once in a lifetime adventure.