It comes after Saturday's shocking attack on London Bridge, in which three jihadis wreaked havoc armed with knives after deliberately ploughing a vehicle into revellers enjoying a night out.
The unidentified suspect pulled the hammer from his backpack and injured a police officer on duty outside the cathedral, police union spokesman Yves Lefebvre told French news outlet BFM TV.
One posted on Twitter: 'Not the holiday experience wanted. Castaner said it "is very hard to anticipate" attacks when they were staged by people who were not on the police radar. We are with our 2 terrified children'.
Police in the French capital, Paris, have shot and injured an attacker near the Notre Dame Cathedral.
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The fire broke out not long after midnight and when many people living inside the tower block were asleep. Another said how they'd seen a baby thrown from an upper floor and caught by a bystander.
The terrorist was immediately shot twice by the officer he wounded; and although he wasn't killed he was brought down in by the gunfire, according to Fox News.
Although the hour-long operation at Notre Dame has ended, France's counter-terrorism office has opened an investigation.
French interior minister Gerard Collomb told reporters that the attacker, believed to be an Algerian student, was also armed with kitchen knives.
Preliminary information indicated he had acted alone.
Notre Dame, which is situated on the banks of the Seine river in the heart of Paris, draws 13 million visitors a year.
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Lawrence Langner, a 73-year-old American, said he suddenly heard a commotion and two detonations like gunshots.
His rivals portrayed him as weak on security during the presidential campaign.
France remains in a state of emergency after a series of deadly attacks by jihadis across the country since January 2015. Soldiers patrol its streets alongside police to guard tourist sites, government buildings and events.
The incident, which occurred at around 4.20pm local time, prompted a lockdown at Notre-Dame Cathedral.
Dozens of armed police sealed off the area and put the Gothic cathedral into lockdown with almost 1,000 tourists and worshippers inside.
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Conte texts players wishing them a good holiday and telling them to stay fit. "Conte said he did not count on me for next season. Costa is furious at Conte's gesture, with the Spaniard of the view that he should have been told the same in person.
7-9 Jan 2015 - Two Islamist gunmen storm the Paris offices of satirical magazine Charlie Hebdo, killing 17 people.