My tenant passed away 5 months ago. All his furniture is still in the apartment. How can I recover the property to put it back on the rental market?

Unless someone is entitled to request the transfer of the lease (Article 14 of the Law of 6 July 1989), the tenant’s death terminates the rental contract.
However, the furniture belongs to the tenant’s heirs. If they have not come forward to collect it, you must formally notify them through a bailiff (commissaire de justice) in accordance with Article 771 of the Civil Code.
If no heirs are known, you must file a petition with the court to have the estate declared vacant and a curator appointed (Articles 809-1 to 3 and 810 of the Civil Code). The curator will then decide what to do with the belongings: either sell them or dispose of them depending on their market value.