The French interior ministry said that two hostage-takers were “neutralised” in the attack in the town of Saint-Etienne-du-Rouvray.
A second hostage was in critical condition, the ministry added.
French President Francois Hollande and Interior Minister Bernard Cazeneuve were on their way to the scene, their offices said.
The incident comes as France remains on high alert nearly two weeks after Tunisian Mohamed Lahouaiej Bouhlel mowed down a crowd of people celebrating Bastille Day in the southern city of Nice, killing 84 and injuring more than 300.
The attack was the third major strike on France in 18 months and was claimed by the Islamic State group. -AFP