Questions were mounting Friday over how a known Islamic extremist managed to murder seven people, including three children, in three separate attacks before being killed in a firefight.
Adding to pressure on security officials, one veteran police officer asked how the gunman was not taken alive during Thursday's siege and final assault in the southwestern city of Toulouse.
Officers from an elite unit moved in Thursday morning after a 32-hour siege, killing self-proclaimed Al-Qaeda militant Mohamed Merah as he tried to shoot his way out of his apartment.
The siege had interrupted the hard-fought campaign for France's April-May presidential vote, but Sarkozy resumed his re-election bid with a rally in Strasbourg Thursday evening, where he said: "These crimes were not the work of a madman.
"A madman is irresponsible. These crimes were the work of a fanatic and a monster.
In a televised address earlier, Sarkozy had vowed to crack down on extremism, saying he wanted legal action against people who regularly consulted jihadist websites or travelled abroad for indoctrination.
But some politicians were already asking how French intelligence officers had failed to head off Merah's killing spree given that he was already on their radar as an extremist.
Sarkozy's main challenger, the socialist Francois Hollande, referred to reports of possible failings in the surveillance of Merah at a rally late Thursday.
With the end of the siege, he said, "questions will have to be put."
Earlier Thursday, French Foreign Minister Alain Juppe said in an interview with Europe 1 radio that intelligence officers had recently questioned Merah.
While he did not know if the intelligence service was at fault, he acknowledged the matter would have to be investigated.
Friday's edition of the Communist daily L'Humanite called for full disclosure over how closely France's intelligence services had followed Merat's activities in the run-up to his attacks.
And left-leaning Liberation asked if political considerations had influenced how police had handled the crisis.
The more right-leaning Le Figaro said it was right to ask questions, but warned against a rush to judgment.
It denounced the knee-jerk reactions from intellectuals, left-wing politicians and rights activists with no experience of the real issues "who never lose a chance to cry scandal".
Catholic daily La Croix also warned that it was too easy for armchair experts to say what should have been done after the fact. But it called for scrutiny of the intelligence services' role.
The killings have shocked France, home to western Europe's largest Jewish and Muslim minorities.
During the siege, Merah told police he had carried out all three recent attacks. In the first two, last week, he shot dead three soldiers. Then on Monday he gunned down three children and a teacher at the Ozar Hatorah Jewish school.
An Al-Qaeda linked group, Jund al-Khilafah, has claimed responsibility on jihadist websites for the killings.
On Thursday morning, as police from the elite RAID force stormed Merah's apartment, the 23-year-old burst out of the bathroom wearing a black djellaba,
a traditional loose-fitting North African robe, and a bullet-proof vest.
He opened fire on them before jumping out the window of his first-floor apartment, still firing as he fell. Molins said Merah was shot in the head.
"He was dead by the time he hit the ground," one police source told AFP.
Police had been told to do everything possible to take Merah alive, but had had no choice but to fire, said Molins.
And RAID head Amaury de Hauteclocque said: "It's the first time in my life I've seen someone, as we launch an assault, launch an assault against us."
But Christian Prouteau, who founded the GIGN -- another of France's elite police units -- wanted to know why police had not used tear gas to flush out Merah, expressing astonishment that they had failed to capture him alive.
In an interview, with Ouest France newspaper, he asked: "How come the
police's best unit did not manage to arrest a man all alone?"
Merah had said his attacks were to avenge Palestinian deaths and to punish France for its military presence in Afghanistan and the ban on full-face veils, Molins said.
He claimed to have been trained by Al-Qaeda in Waziristan, a tribal area of Pakistan known as a haven for Islamist insurgents connected to Taliban guerrillas.
He had twice travelled to the region, said Molins, on one occasion being arrested by Afghan police and handed over to US army troops. They put him on a flight back to France.
A US intelligence official told AFP that Merah had been on America's "no-fly" list: banned from boarding flights to or from the country.
The Al-Qaeda linked Jund al-Khilafah, claiming responsibility on jihadist websites, said "the Frenchman carried out an operation that shook the foundations of the Zionist Crusaders.
"Israel's "crimes... will not go unpunished," the statement added.
According to US monitoring group SITE Jund al-Khilafah has previously claimed attacks in Afghanistan and Kazakhstan.
Merah had filmed the killings with a camera attached to a chest harness, Molins confirmed Thursday. Officers have viewed the footage.
During the March 11 shooting of a paratrooper in Toulouse, he can be heard saying "You kill my brothers, now I'm killing you", Molins said.
In the March 15 attack, when he killed two other paratroopers in nearby Montauban, after the attack he drives off on a scooter shouting "Allahu Akbar!" (God is Greatest!).
On Monday the gunman, again wearing a motorcycle helmet and riding a scooter, attacked the Ozar Hatorah Jewish school in Toulouse, killing a religious studies teacher, his two young sons and a seven-year-old girl.