Macron said investigators are trying to establish how the suspect obtained the gun used in the attack in Trebes and nearby city of Carcassonne, where officials say the 26-year-old hijacked a auto and claimed his first victim.
"He had been on a watchlist for his radicalisation and links to the Salafist movement", Molins told reporters in Carcassonne, adding that Lakdim had been tracked for his online contacts with extremists.
One of the victims was a French police officer who swapped himself for a hostage.
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.
There are unconfirmed media reports that the assailant claimed connections to the Islamic State group.
French Prime Minister Edouard Philippe said earlier on Friday the French authorities believe that a hostage-taking incident in southwestern France might a terrorist attack judging by its circumstances.
COLD ROOM Witnesses said about 10 people in the supermarket found refuge in its cold storage room.
Lakdim then shot and wounded a policeman who was out jogging with colleagues before driving to nearby Trebes, bursting into a Super U supermarket and shooting a customer and an employee dead.
One supermarket worker said some shoppers had escaped from the building after the gunman shouted "God is greatest" in Arabic. "So I went to see what was happening and I saw a man lying on the floor and another person, very agitated, who had a gun in one hand and a knife in the other".
"He raised his gun and fired, I ran away, he shouted "Allahu Akbar" and spoke about the Islamic State".
That assault marked the first of several big Islamist attacks in France since 2015, including the massacre at the satirical newspaper Charlie Hebdo, the November 2015 attacks that killed 130 in Paris, and a summer 2016 truck attack during Bastille Day festivities in Nice.
But in recent months, support for the French leader has dropped in the polls.
The IS-linked Aamaq news agency said the attacker was responding to the group's calls to target countries in the US -led coalition carrying out airstrikes against IS militants in Syria and Iraq since 2014.
"THE THREAT IS EVERYWHERE" France is part of a USA -led coalition fighting Islamic State in Syria and Iraq and has thousands of soldiers in West Africa fighting al Qaeda-linked militants.
Nearly six years ago to the day, Islamist gunman Mohammed Merah killed seven people in the Toulouse region, about 90 km from Carcassonne. That forced many passengers to cram into the-overcrowded-trains that were running.