No. By renouncing the succession of your father, you lose the title of heir in his succession. Consequently, you are not bound by any debt obligation, but in return, you lose all rights to his property.
As the lease is automatically terminated following the death of your father, since no beneficiary can claim its transmission, the lessor will have to turn to the president of the court of law to be authorized to empty the premises and store the furniture in another place (article 1324 of the Code of Civil Procedure).