Perhaps I can help you a little with the grooming part. I run a dog grooming shop in Eymet which I took over two years ago. www.shampoochiens.net
.I had to register with the Chambre de Metiers as an artisan. I do not know if there is a recognised qualification here in France to allow one to work as a groomer hower I took along my city and guilds and they accepted that OK. You will find grooming a very different kettle of fish here. The french, and you will need to work with the french, 70% of my clients are French, (yes even in Eymet!) do not have their dogs groomed as often as the British, and some dogs come in in the most horrendous state. One just smiles and gets on with it. Most clients do not book the next appointment as in the UK and expect you to be able to do the dog on the day that they ring up.
Mine is a shop rather than a mobile, and I am sure that there are people on here who know about running a mobile business. I believe that you have to have permissions from the Mairie's if you wish to park up and work in their communes at markets and things.
If you are running two businesses between you will have to pay two lots of cotisations unless one business is less than 15% of the turnover than the other.
If I can help at all with questions you have please contact me privately.
Canouan English Springer Spaniels and Affenpinscherswww.canouan.co.ukhttp://canouan.chiens-de-france.com