If you walk right round Mont Blanc once in either direction,
then you have done the Tour du Mont Blanc.
You will probably not have walked a lot on the Mont Blanc Massif itself, since the going would be rather hard! Your route will have taken you along the mountains which skirt it.
In days gone by, your route would have probably have used quite a lot of vehicle roads. Now there are new paths which are much more fun: for example the high path from just above la Fouly to la Peule (both in Switzerland) which avoids a section on the road.
The French IGN maps do have a continuous route marked on them and it is labelled the Tour du Mont Blanc, but then they needed to mark something didn't they? You will also find they mark some other paths as "Variants" and there are some splendid paths marked as "Tour du Pays du Mont Blanc". The latter tend to be rather longer and, in places, take some attractive routes.
You may have heard of the "Ultra Trail du Mont Blanc". This is an annual race around the TMB. The winner will take less than 24hrs to complete it, running non-stop! The route chosen will be specially-marked for the occasion and will need to stay on the wider paths, since there are normally over 2000 runners.