Since writing Part 1 of the finances section I have had second thoughts. I might be deterring people from relocating to France unnecessarily, so I will present a couple of options here if you have limited funds available. Part 1 was assuming that you needed to have enough funds to spend the rest of your life in France, but that needn't be the case. Even if it doesn't work out, you will have had a new experience for a couple of years, which will surely be a good thing. So other options are...
Rent don't buy
Don't buy a property straightaway. You can rent for a couple of years first, while you try to get a business off the ground. Annual rent in rural locations is not high, although in many areas there is a shortage of properties available to rent.
This could be developed into 'buy a complete wreck but do a lot of the renovation work yourself, however long it takes'. Possibly living on site in a caravan or similar during the work. This approach would also enable you to live in France at significantly less cost than buying somewhere outright.
Work from home
Establishing gites or a bed and breakfast business is expensive. If you are to earn 20,000 euros a year you will need to spend 200-300,000 euros up front. But of course many businesses do not require that level of expenditure.
Copywriting, internet based businesses, salesmen covering France or Europe, labouring, writing articles for magazines, translations, website design, writing novels, financial research, teaching English to French people, etc. etc. are all jobs that expatriates in France have, without having spent significant money up-front.
If you have a talent or strength that you could develop into a business that does not need you to 'go to work' every day and you can work from home, you could pursue this and have a successful business up and running reasonably quickly.
Taking these two things into account, and assuming that you may need to return to your home country if the business is not a great success, I think you could probably move to France, rent a house and start a business, with as little as 50,000 euros total (to see you through a year or two) or even less if you have a business already that could be transferred. A bit easier than my original conclusion!
An introduction: Living in France
Financial considerations: Finances of moving to France
Moving on a limited budget / how little money can you move with: Relocating on a budget
Language considerations: problems with learning the language: Language problems for expats
Meeting people and becoming established: living in a French community
Schools and education: expat children in French schools