An individual can be a sole trader (Enterprise Individuelle) or can be a EURL (Enterprise Unipersonnelle a Responsibilité Limitée) which is a private limited company with one shareholder.
From 1st January 2009 a simplified system of setting up a business called "auto-entrepreneur" became available with fixed taxes and cotisation based on turnover (limited to that of microenterprises below).
If the entrepreneur meets certain conditions they can be a Microenterprise where accounting requirements are less onerous but tax returns still have to be made.
The main condition to fulfil to be a microenterprise is maximum earnings of 32,600 euros for services and professions and 81,500 euros for commerce and if you qualify you can use a fixed deduction as high as 72% to arrive at taxable income and be exempt from VAT registration.
Such a Microenterprise may be suitable for income from furnished holiday lettings.
A partnership or other form of multiple ownership is more complex and the two most common forms are the SARL (Société a Responsibilité Limitée) which equates to the UK small company with a minimum of two shareholders and limited share capital and the SA (Société Anonyme) which is a larger company requiring more shareholders and a larger share capital commitment.