Mr. Paty, 47, was “assassinated”, said the French president.
The history teacher, who allegedly discussed the images of the Prophet Muhammad with his students, was beheaded, it was reported.
The suspected attacker was shot dead about 600 meters from the scene, according to the AP news agency.
It happened in a street in Conflans Sainte-Honorine, north-west of the French capital, around 5 p.m. local time.
While visiting the place, Emmanuel Macron described it as a “cowardly attack”, saying that the man was “the victim of an Islamist terrorist attack” and had been killed because he “taught freedom of expression, to believe and not to believe ”.
The president said France would “protect and defend” its teachers.
According to Le Parisien newspaper, the attacker was an 18-year-old man of Chechen origin, who carried a knife.
Sky’s Adam Parsons, who is at the scene, says he was not on any watch lists.
He was reportedly shot dead after refusing to put down his weapon.
A video of his final moments is believed to feature the sounds of the gunshot, followed by a volley of gunfire as he was killed.
A gun was found next to him. Reports say it was an airsoft gun that fired plastic pellets.
The country’s counterterrorism prosecutor previously called the incident a stabbing, but Reuters and AP news agencies said police sources told them the victim was beheaded.
Witnesses heard the attacker shout “Allahu Akbar” or God is great, Reuters said.
French counterterrorism prosecutors said nine suspects were also arrested, including the attacker’s grandparents, parents and 17-year-old brother.
Mr Paty is said to have shown pictures of the Prophet Muhammad in class during a discussion on free speech on October 5.
A complaint was filed and the teacher was then contacted by the police.
Sky News understands that among those who complained was a relative who posted a video online about the incident. This parent is one of the nine arrested.
The suspect had no children in school, AP said.
A Twitter thread posted last Friday, suspected students had seen caricatures of the prophet.
However, another parent of one of the teacher’s students said Mr. Paty asked the Muslim students to raise their hands and leave the classroom before learning more about the picture.
She said: “My son understood right away – the night he came home he understood straight away that it was not about discrimination.
“He said to me, no it wasn’t to offend us, it was pictures he didn’t want us to see. My son understood that at no time had he (the teacher) been disrespectful. “
The Minister of Education, Jean-Michel Blanquer, tweeted that the republic had been attacked by “the despicable murder of one of his servants”.
He added that “unity and firmness are the only answers to the monstrosity of Islamist terrorism”.
British Foreign Secretary Dominic Raab tweeted to express the government’s solidarity with France: “My thoughts are with the people of Conflans-Sainte-Honorine tonight following reports of a truly horrific attack. The UK stands in solidarity with France at this time. ”
This is the second terrorism-related incident since the opening of an ongoing trial over the January 2015 newsroom massacre at the satirical newspaper Charlie Hebdo after the publication of caricatures of the prophet of Islam.
At the start of the trial, the newspaper republished cartoons of the prophet to emphasize the right to free speech.
Exactly three weeks ago, a young Pakistani man was arrested after stabbing two people outside the newspaper’s former offices with non-fatal injuries.
The 18-year-old told police he was shocked by the publication of the cartoons.