Following this post with interest. Have never thought about doing this before as thought it would be too high/difficult, but maybe not...
I would say that if you can do walks in the Lake District e.g then you can do the TMB. Yes, it's quite high up but then again you're starting every day usually higher up than Scafell Pike or Ben Nevis. The paths are all in good condition and the TMB is well signposted throughout. I just wish I'd done it 20 years ago.
I met many groups and individuals doing the walk of all shapes and sizes, including a group from the U.S. who were all over 69. It was a tough old slog at times but so are many of the walks here, the scenery is a great reward though for the effort and there are alternative routes on some days if you get a good weather day and want to go higher.
They have their own website (with English alternative) at
http://www.autourdumontblanc.com/en/ which lists nearly all of the Refuges (Hostels) and gives the distances between them in hours making it easy to plan, many of which you can book online via that website. Some towns/villages also have Hotels if you prefer.
It's a cracking walk if you get the weather that I got and are physically fit enough to do bigger hills on multiple days, you can take optional rest days along the way in places like Courmayeur or Champex.
I'm having a few days off before I get my website updated with photos and a trip report etc