The State Council said it would decide before the summer in the case of Vincent Lambert, who has been in a vegetative state since a car crash in 2008.
The court said it had ordered a team of three doctors to carry out tests to determine the "irreversible nature" of Lambert's condition.
"Given the urgency of the situation, the State Council is asking the experts and consultants it has named to hand in their report within two months," said the council's vice-president, Jean-Marc Sauve.
Doctors treating Lambert, as well as his wife, want to cut off intravenous food and water supplies but his deeply religious Catholic parents and other family members oppose the decision and took the matter to court.
A court in Chalons-en-Champagne near Reims ruled against ending his life last month and the case was brought to the State Council on appeal.
A 2005 law in France legalised passive euthanasia, where a person causes death by withholding or withdrawing treatment that is necessary to maintain life.
The French case comes amid often heated public debates in Europe over euthanasia, including in Belgium where lawmakers voted Thursday to extend the right to die to terminally ill children.