Lucien Abdelrhafor, 20, also received part of a suspended sentence for telephoning the threat Monday, the French newspaper L'Express reported.
The SPCJ, the protective service of the Jewish community in France, said a man called the Ohr Hatorah school in September and said, "I am Mohammed Merah's cousin and I'm coming over tonight to kill you," a reference to the person who shot four people at the school in March 2012.
Abdelrhafor is not Mehar's cousin, SPCJ said, adding French police arrested several people who threatened violence against the school after the shooting.
The school changed its name from Ozar Hatorah after the attack, the Jewish Telegraphic Agency reported.
Senate Democrats to pull all-nighter on climate change
Jessica Simpson shares three-way kiss with friends in photo