The man, 23, was arrested at an air base in Lyon after relatives told police they found suspicious documents in his possession, Radio France International reported Monday.
The Interior Ministry said charges against him include planning to damage a place of worship "in connection with a terrorist enterprise."
Investigators said the soldier told them he planned to fire shots at a mosque in Venisseux, a Lyon suburb, on the last day of Ramadan.
He also admitted to throwing a firebomb at a mosque in southwestern Libourne in August 2012.
News of the arrest raised fears of increased attacks in the Muslim community.
"The fact that he is from the military shocks me," said Kamel Arioua, president of the Essalem association that supervises mosques in the Lyon region.
"Luckily, he was caught just in time," Arioua added. "If not, the day of Eid would have been a day of carnage, after there were already some riots."
Alexandre Gabriac, former president of the Young Nationalists, an extreme right-wing group, blamed the government for the aborted attack. The government's ban on all nationalist groups "is pushing people to make rash and unilateral decisions," he said.