PARIS—French authorities believe Hayat Boumeddiene, the girlfriend of the gunman who was killed during a police raid at a kosher store on Friday, left France Jan. 2 and has reached Syria, people familiar with the matter said Saturday.

Police have been hunting for Ms. Boumeddiene since her partner, Amedy Coulibaly, was identified as the alleged shooter of a policewoman on Thursday and stormed a Parisian kosher grocery on Friday, leaving four hostages dead.

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