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No one is said to have been hurt, but the fire damaged much of the Promo & Stock store.
Antoine Besme of the regional prosecutor's office said authorities believe the fire Tuesday in the suburb of Creteil was of a criminal nature, because the store's protective shutters had been forced open.
Besme told The Associated Press that a preliminary investigation was opened, and that authorities are working to see if there is a link to last week's vandalism.
The fire raised concerns because of the anti-Semitic graffiti, and because the fire broke out three years after a deadly Islamic extremist attack on a kosher market in Paris.