Thank you for the addition and important information. In French law, there are basically to laws that govern renting situations between tenants and owners, a law concerning rent for habitation (home) purpose and the rent for business purpose. In French law, it is possible to rent and apartment or house to an individual (non business) who plans to run a business from the rented home. According to what I understand this is the situation you are in. French law, French municipal law, and home owner’s organizations may prohibit the use of the home for business purposes. Assuming that it is allowed and that you as the owner is granting use of the home for business purpose too, then the terms of the rent agreement that you mentioned would be valid.
Your first question is : “Is it possible to grant a 6 months furnished tenancy with a 3 months notice of requirement of possession - tenant will be occupying and running a business activity?” In French law, for a furnished tenancy, the minimum amount of time of notice is one month. A minimum of 3 months notice is for non furnished tenancy. However, you can grant a 3 months notice for a furnished tenancy if you want.
Your third question is : In this type of tenancy what would be the problems if the tenant does not pay the rent or refuses to leave after proper notice.
If the tenant does not pay the rent or refuses to leave after proper notice, that in itself would be a problem for you. You will have to start legal proceedings (in court) to get the tenant to vacate the premises. You will need a court order to get the police to help you. The French police will not do anything without a court order. This can take several months, even years depending on the degree of stubbornness and bad faith attitude of the tenant and the period of the year involved. Most of the time the court will grant the tenant a certain amount of time to pay back the late rent in small payments and allow the tenant to remain in the apartment or house. In French law it is impossible to kick a non paying tenant out between the months of November and March. Most tenant know this and organize their bad faith attitude around these dates. Each bad faith tenant reacts differently and uses different strategies to remain in the rented place. In French law the owner can not just go and kick the tenant out of the house, put the tenant belongings on the sidewalk and change the keys. This is illegally. However there are stories of owners who do not want to go through the long lengthy and costly legal court process who break the law by changing the keys and putting the tenants belongings on the street. Not only this is illegal, but the owner will have not court order to collect unpaid rent. With a court order to collect unpaid rent, one can garnish the renter’s bank account, seize their cars, tv, etc…
This answers your second question : "If tenant does not vacate at end of tenancy how long would it take to regain possession for whatever reason or to sell or personally to re-occupy Would it mean relying on a long court process?" Yes, it would mean relying on a long court process.