This is announced by France's Minister of the Interior Bruno Retailleau on Thursday.
It was on Monday that the man, a homeless man of Moroccan origin, lit the cigarette at the grave monument where a flame burns to honor French fallen soldiers.
The incident, which has aroused outraged feelings in the country, was filmed by a tourist who was at the monument at the time.
The man was arrested by the police and is detained, suspected of desecration of a cemetery, a crime that can result in up to one year in prison and a fine of 15,000 euro.
"This shameful and despicable act undermines the memory of those who have died for France", wrote Minister of the Interior Retailleau on X.