French police have killed a man after a synagogue was set on fire in the north-western city of Rouen.
The man was armed with a knife and a metallic tool and was shot after he threatened officers, the Rouen prosecutor said.
Rouen Mayor Nicolas Mayer-Rossignol said the attack on the synagogue did not just affect the Jewish community, but the entire city was "battered and in shock".
French reports say the suspect was Algerian and was appealing against an order to leave France.
Police were called at around 06:45 (04:45 GMT) after smoke was seen rising from the synagogue. The attacker climbed on a large waste bin and threw a petrol bomb through a small window, setting the synagogue alight.
Two police officers reached the scene fast, after the man was spotted on security cameras. The suspect was on the roof of the synagogue when they arrived, according to prosecutors. After threatening the pair he then threw a chisel at them before jumping down to the ground, brandishing a knife.
"The officer opened fire five times, hitting the individual four times," said Rouen public prosecutor Frédéric Teillet, explaining that he had seen the footage on the security cameras.
Firefighters at the scene eventually brought the fire under control inside the synagogue in the historic centre of the city. There appeared to be no victims other than the armed man, the mayor said.
Damage inside the synagogue has been described as significant. "I'm really upset, it's catastrophic," said the head of Rouen's Jewish community, Natacha Benhaïm.
The walls and furniture had been left blackened by the fire, although "the Torah scrolls, the holy books, did not come to any harm".
Mr Teillet said two investigations were under way - into an arson attack on a place of worship and into the use of a police weapon outside the building.
Although the officer was currently in custody, the prosecutor said that video footage indicated he had used his gun "according to conditions allowed by the internal security code".
Interior Minister Gérald Darmanin praised police "for their responsiveness and courage ".
Little is known about the suspected attacker, who was not carrying any form of identity at the time. French media report that he was a 29-year-old Algerian who was in the process of appealing against an expulsion order from French authorities.
France, in common with the rest of Western Europe, has seen a surge in antisemitism since Hamas attacked southern Israel last October leading to the current war in Gaza.
Earlier this week a memorial in Paris that honours 3,900 men and women who helped rescue Jews during the Nazi occupation of France in World War Two was daubed with red-painted hands.
President Emmanuel Macron said defacing the wall undermined the memory of France's heroes and its victims of the Holocaust.
France has the third largest Jewish community in the world, after Israel and the US.
The head of France's Council of Jewish Institutions (Crif), Yonathan Arfi, said that "setting a synagogue on fire - that's intending to intimidate every Jew".
Another leading figure in the Jewish community, Elie Korchia, thanked police for their quick response to "a new antisemitic drama in our country".
Rouen's places of worship have come under attack in the past. Eight years ago a priest was fatally stabbed while leading a church service.
The latest violence comes days after gunmen shot dead two prison officers in an ambush at a motorway toll south of the city. Convicted prisoner Mohamed Amra escaped during the attack and his still on the run.
