I found out that all the heirs of my tenant who died 6 months ago have decided to renounce his estate. The apartment is still furnished with furniture from my former tenant. Can I get rid of it?

No. A landlord cannot himself recover the accommodation and get rid of the furniture of his deceased tenant. When there is no known heir and if the rental contract has ended, the owner must first obtain a court decision (article 1324 of the Code of Civil Procedure).
The costs of removal and conservation of furniture are to be advanced by the owner.
To recover the costs and any unpaid rent, the lessor will have to turn against the estate or, if the estate is unclaimed or vacant, it will be up to him to seize the president of the judicial court through a request in order to obtain the appointment of a provisional administrator of the Domains who shall manage the succession (article 809-1 to -3 and 810 of the Civil Code).