The French interior ministry said that two hostage-takers were “neutralised” in the attack in the town of Saint-Etienne-du-Rouvray.
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 over 300.
The attack was the third major strike on France in 18 months and was claimed by the Islamic State group.
In France, the Normandy attack comes 12 days after a 31-year-old Tunisian Mohamed Lahouaiej Bouhlel plowed his heavy goods truck into a crowd of revelers in the French Riviera city of Nice, killing 84 people. Islamic State claimed that attack.
The knifemen launched their assault by taking five people hostage inside the church in the Normandy town of Saint-Etienne-du-Rouvray, south of Rouen.
French President Francois Hollande was on his way to the site of the attack.
“Horror. Everything is being done to trigger a war of religions,” tweeted Jean-Pierre Raffarin, a former conservative prime minister who now heads the Senate’s foreign affairs committee. – Agencies