British Prime Minister Theresa May hailed Beltrame's courage and sacrifice on Twitter, saying they would never be forgotten.
French police officers cordon off an area during the hostage-taking in Trebes.
Mr Macron said investigators will focus on establishing how Morocco-born Lakdim obtained his weapon and how he became radicalised.
Some of the hostages managed to leave the supermarket before the police arrived.
Col. Beltrame had taken part in an eerily similar training scenario in the same region just a few months beforeWhat was Beltrame's background and what training session did he organise? '#ArnaudBeltrame' was a trending topic on the social network where people expressed their respect and gratitude for the officer, and thoughts for his wife.
Beltrame's entire career seemed to lead inexorably to the moment when he responded to the attack Friday in Trebes, a 15-minute drive from the gendarme unit he had led since August.
Lakdim was known to authorities for drug-dealing and other petty crimes, but had also been under surveillance by security services in 2016-2017 for links to the radical Salafist movement, Paris prosecutor Francois Molins said on Friday.
Singapore condemns the terrorist attack in France, the Ministry of Foreign Affairs said in a statement yesterday. At the time, he equipped his policemans with paintball weapons, inning accordance with Depeche du Midi, the regional paper. Lakdim acted alone, starting early Friday morning near the city of Carcassonne, stealing a car and killing its owner. We are with you @EmmanuelMacron!' he added.
Across the Atlantic, U.S. President Donald Trump said Sunday on Twitter the deadly shooting in southern France showed the need for stronger measures in the fight against the Islamic State group, including border security.
Lakdim requested the release of Salah Abdeslam, the sole surviving assailant of the November 2015 attacks in Paris that left 130 people dead.
Samia Menassi, the manager of the supermarket targeted in the attack, said her colleague who was swapped for Lt Col Beltrame during the siege was in a catastrophic state.
Beltrame had left his phone on so police could hear his interactions with the gunman, Collomb said. He then drove to the nearby town of Trèbes, not far from Toulouse, where he stormed into a supermarket, opened fire and held employees and customers hostage for several hours. The fact is that he did not hide his faith, and that he radiated it, he bore witness to it. We can say that his act of self-offering is consistent with what he believed.
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"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 abroad, said.
"He was yelling threats at people, 'Everybody on the ground'", Mr Guibbert said.
The gunman then shot at four National Police officers who were jogging in Carcassonne.
Hundreds of tributes have poured in since the brave officer's death.
He later on educated for the elite GIGN police that is experts in counter-terrorism as well as captive rescue, and also at one factor educated to become an army freefall parachutist, a sort of high-altitude parachuting usually executed by special forces.