Citing a statement of the interior ministry, the daily Le Parisien said the 23-year-old soldier, who was arrested on the airbase Lyon Mont Verdu, attacked a mosque with a Molotov cocktail last year.
No casualties were reported in the attack.
“The interior minister reiterates his determination to fight against all forms of violence inspired by the most extremist ideologies that affect the values of the Republic and whose sole objective is to create tension in the society and propagate a climate of hate,”the ministry said.
“No violence will be tolerated,” it added.
In a move to crack down on fascist cells, “that are against the values of the Republic,” the government shut down five far-right groups last month.
The government had launched a dissolution process after a young anti-fascist activist, Clement Meric, was killed in June during a fight with the Revolutionary Nationalist Youth (JNR) supporters.