The attack happened around 6am on Monday when the unidentified man – who was shouting religious slogans – threatened staff outside the main Police Commissariat in the town of Cannes.
An investigating source said: “He pulled open a car door and started stabbing.
“It was only thanks to officers wearing bullet proof vests that none of them were injured.
“The driver of the car tried to pull away, while another on the back seat of the car opened fire, and the man was severely wounded.
“He had been shouting religious slogans referring to the Prophet throughout the attack.
“The knifeman is now in a critical condition in a hospital in Cannes.”
French Interior Minister Gerald Darmanin tweeted: “A policeman from the Cannes was stabbed and wounded.
“The assailant was neutralised by his colleagues.
“I am going there immediately this morning and I give all my support to the National Police and to the town of Cannes.”
France has seen a wave of stabbings and violent crime over recent months.
In July, an 18-year-old man was shot and three others were injured following a stabbing in Marseille, France.
Back in May, a knifeman was arrested after a policewoman was stabbed several times in a brutal attack near Nantes.
The gunman quickly fled the scene, prompting a huge police hunt.
The policewoman was reported to be aged in her 40s and seriously injured in the leg, arm and hand, according to French media.
Police later confirmed they had made an arrest, while gunshots “were exchanged”.
Police officer Eric Masson was shot dead earlier in May after being called to investigate a known drug-dealing site in the southern city of Avignon.
In April, officer Stephanie Monferme, was also killed in Rambouillet.
These attacks lead to Stanislas Gaudon, head of the Alliance police union, calling for change.
She said: “It was the straw that broke the camel’s back.
“It was something we were afraid of, almost expecting.”