If you want to move to France and to set up a new business or work within your profession, then you are able to apply for a special type of Long Stay Visa/Residency Permit which will issued under the category ‘entrepreneur/profession libérale’ (self-employed in regulated ‘liberal’ profession).
If you are planning on setting up a new business in France, such as running a gite or B&B then you must be able to demonstrate the economic viability of your project. So this would entail providing a detailed business plan with financial projections and/or demonstrating that you have sufficient savings or other income sources to support you. There are also ‘talent visas’ for highly skilled entrepreneurs.
Source: Leonetti Business Services (LBS)