French authorities said police on Friday shot dead a man armed with a knife and a crowbar who was trying to set fire to a synagogue in the northern city of Rouen.

"National police in Rouen neutralised early this morning an armed individual who clearly wanted to set fire to the city's synagogue," Interior Minister Gerald Darmanin wrote on X, formerly Twitter.

Sources told French media the man "was armed with a knife and an iron bar, he approached police, who fired. The individual died."

Local officials said there were no victims other than the attacker.

The synagogue stands in the historic centre of the city, the capital of the northern region of Normandy that lies along the River Seine.

Two separate investigations have been opened, one into the fire at the synagogue and another into the circumstances of the death of the man killed by the police, Rouen prosecutors said.

Such an investigation by French authorities is automatic whenever an individual is killed by the police. (AFP)