Regarding running a business, check carefully as there are many rules and regs to abide by and possible social charges to pay. France is totally different to the UK where businesses are concerned and is very regulated and controlled by different caisses.
Something else to factor into your planning, then, is the need for a visa and to be able to prove that you’ll draw sufficient income from it to satisfy the requirements (roughly that you can earn at least the equivalent of SMIC, the minimum wage). Brexit made the alternatives very stark: either you have a “proper” income or you can’t work!
Based on your plans, while I wouldn’t rule out France, there may be other countries within Europe that would be more amenable to running a business and also have a significantly lower cost of living. That’s not to say you shouldn’t do it, and if you’re someone who likes a carefully regulated environment then it might actually seem a great place. But it’s also not somewhere you can just rock up with a laptop and internet connection and ‘work from home’.