A priest was killed on Tuesday when men armed with knives seized hostages at a church near the northern French city of Rouen, a police source said.
Police said they killed two hostage-takers in the attack in the Normandy town of Saint-Etienne-du-Rouvray, 125 kilometres (77 miles) north of Paris.
A priest was killed and another hostage was "between life and death", the interior ministry said.
The motivations for the hostage-taking were not yet clear, but the Paris prosecutor\’s office said the case had been handed to anti-terrorism judges for investigation.
The incident comes as France remains on high alert nearly two weeks after Tunisian Mohamed Lahouaiej Bouhlel ploughed a truck into a crowd of people celebrating Bastille Day in the French Riviera city of Nice, killing 84 people and injuring over 300.
French President Francois Hollande, who is from Rouen, and Interior Minister Bernard Cazeneuve were on their way to the scene, their offices said.
Footage showed several emergency vehicles at the scene and the streets sealed off.
The Nice attack was the third major strike on France in 18 months and was claimed by the Islamic State group.
Two attacks in Germany claimed by the Islamic State group since then have also increased jitters in Europe.
After the attack in Nice, France extended a state of emergency giving police extra powers to carry out searches and place people under house arrest for another six months until January.
It was the fourth time the security measures have been extended since Islamic State jihadists struck Paris in November, killing 130 people at restaurants, a concert hall and the national stadium.
The Nice massacre has triggered by a bitter political spat over alleged security failings, with the government accused of not doing enough to protect the population.
Prime Minster Manuel Valls had warned earlier in the week that the country will face more attacks as its struggles to handle extremists returning from jihad in the Middle East and those radicalised at home by devouring propaganda on the internet.
France has been concerned about the threat against churches ever since a foiled plot against in the Paris suburb of Villejuif in April last year.
Sid Ahmed Ghlam, a 24-year-old Algerian IT student, was arrested in Paris on suspicion of killing a woman who was found shot dead in the passenger seat of her car, and of planning an attack on a church.
Prosecutors say they found documents about Al-Qaeda and IS at his home, and that he had been in touch with a suspected jihadist in Syria about an attack on a church.