Doctors treating Lambert, 38, want to cut off intravenous food and water supplies and Lambert's wife agrees with them.
But his deeply religious Catholic parents opposed the decision and took the matter to court.
The Council of State on Friday has ordered a new experts' opinion and promised to reach a decision "before the summer ... given the extreme seriousness of the situation".
In 2005 France legalised passive euthanasia, where death is caused by withholding or withdrawing treatment that is necessary to maintain life.
The doctors wanted to take the step on the basis of this law.
But last month a French court ruled against ending Lambert's life.
This comes after months of debate surrounding the legalisation of active euthanasia, which President François Hollande promised to do before the end of the year.
Hardline Catholics oppose it and called on the Pope to raise the matter when he met Hollande last month.
The final decision on the Lambert case will have "a national impact", legal official Rémi Keller commented this week.
The practice is already legal on Luxembourg, Belgium, Switzerland and the Netherlands.
This week Belgium legalised euthanasia for minors.