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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London Fire Commissioner Dany Cotton said : "In my 29 years with London Fire Brigade I have never seen a fire of this nature". Fire crews are continuing to tackle "pockets of fire" in the building with many people still unaccounted for.
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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But she held, and went on a four-game surge, playing the only way she knows how: from the front foot and going for the lines. She arrived in Paris having reached a final on the WTA tour in each of the last three years but with no title to her name.
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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In the early hours of Wednesday fire broke out around the fourth floor of the building, and within minutes the tower was engulfed. Meanwhile, a spokesman for Theresa May has said that she is " deeply saddened by the tragic loss of life in the Grenfell Tower ".
7-9 Jan 2015 - Two Islamist gunmen storm the Paris offices of satirical magazine Charlie Hebdo, killing 17 people.