The Manchester United striker has been included in the hosts' final 23-man squad and, while his involvement in the tournament is not thought to be in doubt, coach Didier Deschamps expects to be without him in Nantes.
"Martial has pain in his thigh," said Deschamps. "He finished the season late. I will not take any risks tomorrow and it is likely that he will not participate in the match.
"There is no doubt about Martial's participation in the Euros. His thigh problem is muscular fatigue."
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Martial scored 18 goals in all competitions for United in 2015-16, and proved to be a rare bright spark in a disappointing season for United.
Deschamps also confirmed that Lassana Diarra, who was hit with a €10 million fine following a contract dispute on Sunday, will feature in France's penultimate friendly.
France kick off their Euros campaign against Romania at Stade de France on June 10.