Speaking after the attack, Mr Collomb said police found kitchen knives, a hammer and other unsophisticated weapons on the wounded assailant.
Another officer responded by opening fire and injuring the aggressor who was later arrested and hospitalized.
Police sealed off the area in front of the cathedral, where the attacker lay injured on the ground.
Following the incident the Paris prosecutor's office swiftly launched a counter- terrorism investigation.
On a cloudy midafternoon, the esplanade outside the cathedral was crowded with tourists and vendors.
Police sources said the officer sustained minor neck injuries in the assault. The attacker's condition was being evaluated. Michel said the attacker was "neutralized" by police. The officer was wounded, and the attacker was taken to a hospital, police said. "He was not working in conjunction with any body", he said.
France is under a state of emergency imposed after a series of terrorist attacks in 2015 and 2016, mostly claimed by the Islamic State extremist group, that left over 230 people dead. A police official from another union confirmed the age of 40. Investigators asked the public to stir away from the crime scene during investigation.
The incident happened around 4:30pm.
It stands on the eastern end of the Ile de la Cite, built on the ruins of two earlier churches.
About 900 people were inside Notre Dame when the shooting occurred, Karine Dalle, a spokeswoman for the Paris archdiocese, said in a text message, adding that those present were "sitting calmly" and had been told about the event.
Armed police cordoned off the site and the cathedral in central Paris that is visited by millions of tourists every year was locked down during the incident. They were later released one at a time after being searched by police. Looking down from his office, he saw a man inert on the square. He declares allegiance to IS, and police later kill him.
"I thought it was very well-handled, but it makes you think twice", she said.
Shalane Sharples was walking toward Notre Dame Cathedral when she heard "some really loud bangs".
"I think it is a strong signal that we need to work together to get to the bottom of these issues", Soderberg said. "Now everyone just wants to go home".
The attack came the day before President Emmanuel Macron unveils his first efforts against terrorism, which Collomb called the president's top priority.