"We will never forget his heroism, his bravery, his sacrifice. With a heavy heart, I send the support of the entire country to his family, friends and colleagues of the gendarmerie of the Aude," The Guardian quoted Collomb as saying.
Later President Emmanuel Macron issued an official statement saying he was "deeply moved" to learn of the officer's death from his injuries.
Beltrame was shot in the throat at the end of a four-hour supermarket siege in the quiet town of Trebes, near Carcassonne, in southern France on Friday.
He hijacked a car, killed its driver and attempted to mow down four police officers while opening fire at them. One policeman got injured in the incident while he was jogging at a park.
He later drove the car to the supermarket and immediately opened fire upon people, killing two before taking several others as hostages.
It took three hours to bring the situation under control when the police shot dead the gunman in a cross firing.
The militant organisation Islamic State took the responsibility of the attack. (ANI)