The State Council's 17 judges started considering the case of Vincent Lambert today and said it would decide tomorrow whether it will make a ruling or seek further medical evidence.
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.
Lambert has been in a vegetative state since a car crash in 2008.
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The reporting judge who presented the case to the council today recommended further medical tests by three new doctors on Lambert, to be performed within six weeks.
The judge, Remi Keller, said the extra tests were needed as the case has the potential to have a "nationwide impact".
The French case comes amid often heated public debates in Europe over euthanasia, including in Belgium where lawmakers are set to vote today to extend the right to die to terminally ill children.