It's a nice idea but be aware that this sort of arrangement would put you "below the radar", so in a sense, it wouldn't give you an all-round feel for living in France.
From the fisc's point of view, they would want you to pay rent for your accommodation (so that the landlord pays tax on it) and they would expect you to be registered, invoicing and declaring your income for any artisan work you do (so that you pay tax and social contributions on that, and so that there is no "unfair competition" ie taking work awat from qualified paid-up artisans).
It would need to be kept quiet because potentially there could be quite high penalties for this kind of arrangement, and in the longer term it risks complicating your dealings with officialdom because various papertrails will be missing, such as proof of residence in France/rental contract, employment status/where your income comes from/entitlement to health cover, obligatory insurance to cover any 'gros oeuvres' that you might do, professional insurance to cover any accidents that might happen...
Sorry to be a wet blanket but there you go, please don't shoot the messenger, and this reply might in itself help you to "get the feel" for some of the restrictions that are part and parcel of living in France. The attitude to doing a few little jobs 'on the black' is very different from in the UK - of course people do it, but you can't do it too openly.