Police arrested the teenager in the southern city of Toulon on Wednesday after he was reported by a person close to him who was concerned over his radicalism.
Police found several knives at his residence and said the man had threatened to go after those in charge of the weekly, Charlie Hebdo.
He has been taken into custody and charged with "associating with criminals tied to a terrorist organisation", the source said.
The young man recently left high school to reportedly follow a religious practice.
At the same time, police released a man in his forties whom they had arrested Saturday in the western city of La Rochelle for apparently calling to decapitate Charlie Hebdo's editor, Stephane Charbonnier, on a jihadi website.
The weekly magazine published the cartoons Wednesday as often violent -- and sometimes deadly -- protests continued against an anti-Islam film made in the US that has enraged many Muslims.