Remy Martinot froze his father, Dr Raymond Martinot, when he died, at the age of 80, in February this year.
Dr Martinot - a pioneer in the field of cryonics - had in turn frozen his wife when she died of cancer in 1984, in the hope that advances in medical technology would oen day enable the dead to be brought back to life.
But in March a court ruled that keeping the bodies refrigerated at the family chateau was against French law.
The judge said they should either be cremated or buried, and authorised the use of force, if necessary, to carry out the decision.
Mr Martinot appealed, and on Monday, a court in Angers had been expected to give its response.
But instead the court said it would wait to hear whether Mr Martinot will lodge an appeal against a separate ruling, given by an administrative court in Nantes last week, which repeated that the bodies must be buried or cremated.
Mr Martinot and his lawyer, Alain Fouquet, have two months to lodge their appeal.
However, this appeal, and the ruling of the appeal court in Angers, may not be the end of the legal battle.
Mr Fouquet has said that if the appeal fails he will take the case to the Conseil d'Etat - France's highest administrative court - and then on to the European Court of Human Rights.
For now the Martinot parents remain in the cellar of the chateau in the western village of Nueil-sur-Layon.
Cryo-celeb
Raymond Martinot became a much celebrated name in the world of cryonics - the freezing of bodies for possible revival at a later date - after successfully freezing his wife Monique.
It is reported that while he gained permission from the authorities in 1984 to bury her at the family's chateau, they were not aware that he planned to inject anti-coagulants in her veins and place her body in her refrigerator.
He is said to have frequently shown visitors the place where he kept his wife's body, which was kept at a constant temperature of -60C (-76F).
Many European countries have legislation in place restricting the preservation of dead bodies in such a way.
To circumvent such restrictions, those interested in resuming life at a later date have come to an arrangement with cryogenics companies in the United States, where it is permitted in several states.