He was shot by Redouane Lakdim, prompting counter-terror officers to storm the supermarket and shoot the Islamist terrorist dead.
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.
The officer's actions helped bring an end to the gunman's deadly spree, which Macron has dubbed an act of "Islamist terrorism".
During the resulting standoff with police, Lakdim demanded the release of Salah Abdeslam - the only surviving member of the IS cell that attacked Paris in 2015.
Police arrested two people after the attack, one of them a woman connected to Lakdim, on Friday and a 17-year-old man said to be one of his friends overnight, judicial sources said. Find us on Facebook too!
Police stormed into the supermarket and killed the gunman once they heard gunshots inside.
Lakdim started his rampage in Carcassonne at around 10.30am (0930 GMT), hijacking a auto and shooting the two people inside, Molins said.
He then shot at a group of policemen who were out jogging, wounding one of them.
One person died in the carjacking, and two others were killed at the market, the French Interior Ministry said. The officer was also seriously wounded.
Even the French President Emmanuel Macron hailed his sacrifice for the nation and after a meeting with Prime Minister Edouard Philippe said, "He saved lives and honoured his colleagues and his country".
BFM TV reported that the man had shot one person in a auto and injured another before stealing the vehicle.
The police officer had been left fighting for his life after being hit by gunfire inside the Super U supermarket in the town of Trebes.
Macron has said investigators will focus on establishing how the gunman, identified by prosecutors as Morocco-born Redouane Lakdim, got his weapon and how he became radicalized.On Friday night, authorities searched a vehicle and the apartment complex in central Carcassonne where Lakdim was believed to live.
"The death of a Portuguese citizen has been confirmed.by French authorities to our consular services", Miguel Silva, a spokesman for the department concerned with Portuguese living overseas, said.
A woman close to Lakdim was taken into custody over alleged links with a terrorist enterprise, Molins said.
In 2011 Lakdim was found guilty of carrying a prohibited weapon and in 2015 he was convicted for drug use and refusing a court order, Mr Molins said.
The senior officer knowingly put his life on the line after Lakdim was persuaded to swap a female hostage - a deal that allowed the woman to escape but meant nearly certain for the policeman, whose uniform marked him as a living symbol of the "infidel state".
Le Parisien newspaper reported that Lakdim lived with his parents, and quoted a neighbour saying he had dropped off a little sister at school on Friday morning.
Trebes, a tranquil town of 5,000 people along the Canal du Midi, was on lockdown throughout Friday as helicopters swirled overhead and heavily armed and masked police carried out a massive operation in Lakdim's neighbourhood.
Police said he skateboarded to the store and left with two headsets and an Xbox controller that he stuffed inside a red backpack. Gavin Stricker, 19, was arrested later that afternoon for allegedly brandishing a knife on the school bus Monday afternoon.
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