A French citizen being held by Bulgarian authorities is suspected of links to one of the brothers behind the massacre at Charlie Hebdo magazine and will likely be extradited back home, officials said Tuesday.

Fritz-Joly Joachin was arrested on Jan. 1 as he tried to cross the border into Turkey with his young child. French courts had issued a warrant for his arrest based on a complaint from his wife that he abducted their three-year-old and planned to take him to Syria, according to officials and Mr. Joachin’s lawyer. He denies...