Mourad Hamyd, 20, whose sister was married to Charlie Hebdo gunman Cherif Kouachi, was barred from entering Turkey late last month and handed over to Bulgaria's border authorities.
On January 7 2015, the Al-Qaeda-linked Kouachi brothers killed 12 people at the headquarters of the Charlie Hebdo satirical weekly in Paris.
France requested Hamyd's extradition on July 29, accusing him of "conspiring to prepare of acts of terrorism".
Hamyd denied the accusations on Monday, saying he never wanted to go to Syria, denying any links to the Islamic State group that claimed responsibility for the Charlie Hebdo attack. He nevertheless agreed to be extradited.
Sofia City Court's ruling is final and the transfer of Hamyd to France should happen within a week, the court said.
If found convicted of terrorism offences in Frances, he faces 10 years in jail.
He was taken in for questioning and later freed.
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