A tenant may run his/her business from a residential rental and the landlord cannot prevent him/her to do so, providing that:
General information regarding the French legal system
In any purchase of a property in France, consideration must be given at an early stage as there are a number of important issues to take into account such as who is going to purchase the property (you alone? or jointly with your spouse? or though a company? etc.), general and inheritance tax projections, the source of the funds, French inheritance laws, etc.