I have no personal experience with this but you can find some details here. In principle, you should be asked to show that your business is viable and will generate enough income for you. You also need to show that it will obey all applicable laws, that you have enough money to start it and a place to run the business from (e.g. if it's a shop, you can't just say “I want to run a shop”, you need a rental contract for a suitable commercial property) and all the required qualifications/diplomas (for regulated professions).
Once in France, you will need to deal with all the formalities to start a business (depending on where you come from, you might find that's a little more bureaucratic than what you are used to) and go to the préfecture to turn your visa in a temporary residence permit. You have to do that within two months of entering France.
This permit (carte de séjour) is typically valid for one year and replaces the visa (it's one year from the date you applied, so when you get it it will already be several months old). The site is not really clear on what you need to renew it after the first year, you should make an appointment well in advance and will be informed of the documents you need to bring, which will depend on your status.
The treatment you can expect will depend a lot on where you are in France. Some préfectures are overloaded/understaffed and/or generally unpleasant to deal with (the ones I have some experience with are OK but I have read that some préfectures around Paris, like Bobigny, are really horrible).