If you want to live and work in France, and you're an EU, EEA or Swiss national, there's no paperwork to do. You have the right to work, and the right to self-employment. You'll need to get a job, or get your business started (with any relevant permits or regulatory authorisations), but that's it.
If you come from elsewhere, you need to get the right work permit and visa sorted out before you come. For anyone who is being transferred in-company, or has successfully applied for a job in France from abroad, this will mean getting your employer in France to arrange a permit with DIRECCTE (and to start the process for any accompanying family members at the same time); once your work contract has been approved, it goes to OFII (the immigration authority), and it will then be sent to the French embassy or consulate in your home country, where you need to apply for your visa.
Things have been changing in recent years. 2016 saw the introduction of a 'Talent Passport' scheme, with varying requirements depending on exactly which section you use, which applies to skilled recent graduates, employees of innovation companies, scientists, artistic professions, and others. It's particularly useful for higher earners and entrepreneurs, and includes holders of EU Blue Cards (who need to earn at least 1.5 times the French average salary - that adds up to about EUR 54,000 a year).
There's also a category for those with an international reputation - that could apply to technology innovators, museum curators, or writers and journalists, for instance - as well as one for those who want to create a business. They need to commit at least EUR 30,000 of investment in commercial, artisan or industrial activities, and provide a convincing business plan.
It's also possible to apply for a seasonal working permit, but the restrictions are tight; the contract needs to be for more than three months and less than six, and you can't bring your family. Good for single ski instructors or windsurfing professionals - not so good for middle managers with children.