The man was known to police but not considered a terror threat, according to French Interior Minister Gerard Collomb.
Christian Guibbert, a shopper that escaped Lakdim at the supermarket, described his assailant as a "very agitated man shouting several times 'Allahu akbar'".
The BBC reported that the attacker was heavily armed. "We've paid the price of the danger of the terrorist threat in blood for several years".
"I want to tell the nation tonight of my absolute determination in leading this fight", Macron said.
ISIS claimed responsibility for the bloody attack through its Aamaq news agency late Friday, announcing that Lakdim carried out the attack in response to the terrorist group's call for attacks in countries participating in the USA -led military coalition in Syria and Iraq. Amaq offered no evidence ISIS had any contact with the attacker.
"Now mainly internal, it is first of all the result of radicalised individuals living in our country", he said.
Lt-Col Beltrame, who was in his mid-40s, was a qualified parachutist who served for a time in Iraq in 2005 and also worked as part of the elite Republican Guard that protects the French president's Elysee Place offices and residence in Paris, Mr Macron said.
CNN could not independently confirm the gunman made the demand.
The incident has brought a renewed sense of fear among the citizens of France, as they have faced their fair share of terrorist attacks over the past few years.
During the standoff, Lakdim requested the release of Salah Abdeslam, the sole surviving assailant of the November 13 2015 attacks in Paris that left 130 people dead, the minister added. The group lost its strongholds in Mosul and Raqqa previous year.
Following that, he opened fire on police officers while they were jogging in Carcassone, injuring one person.
Police in helmets and body armour took up positions around the supermarket before storming the premises and killing the gunman.
The gunman reportedly voiced his support for the Islamic State while taking hostages in the quiet town..
Swat teams from neighbouring areas were sent to provide support to local police and there are helicopters flying over the area above the supermarket.
A lieutenant-colonel swapped himself in exchange for one of the hostages, Collomb said, adding that the 45-year-old had been seriously wounded.
French special police forces arrive to perform a search operation at the Ozanam housing estate in Carcassonne, southwestern France on March 23, 2018.
The order of the shots was unclear, Collomb said.
The family's apartment was raided by police on Friday afternoon.
Survivors of the supermarket siege said he shouted "Allahu Akbar" and identified himself as a supporter of Islamic State willing to die for Syria.
Sixteen people were injured in the attack.
Macron earlier paid tribute to the bravery of the police officer.
Macron said he would return to Paris in the coming hours and will follow closely the situation.