Khaled Zerkani has links to suspects in the Paris and Brussels attacks.
The video closes with an image of Prime Minister David Cameron with crosshairs over his face.
Abdelhamid Abaaoud, a Belgian national of Moroccan origin, reportedly had plans to strike Jewish targets, schools and the French transport system.
The French government confirmed that alleged ringleader Abdelhamid Abaaoud is dead.
Paris prosecutor says the precise number dead in Wednesday's raid is unclear.