Nicolas Sarkozy relaunched his re-election bid Thursday after French police shot dead a militant who carried out a string of hate killings, hoping his reputation as a crime fighter will carry the day.

The president has been trailing his Socialist rival Francois Hollande in opinion polls for months, but the shocking murders and the killer's violent end have stirred up the campaign just as he was narrowing the gap.

Polls carried out before the crisis showed French voters trust Sarkozy more on security and international affairs, while Hollande gets their vote if they care more about jobs, household incomes or social provision.

Logically, therefore, Sarkozy should expect a bump in the polls as a result of his national leadership during a time of crisis involving a foreign-trained Islamist and a massive police murder manhunt.

But, while Hollande has been cautious, some of Sarkozy's other opponents were quick to allege that the murders were a result of a massive intelligence failure on behalf of Sarkozy's centre-right government.

Far-right flag-bearer Marine Le Pen, stuck at third place in the polls and failing to gain ground, was among the first to break the unofficial campaign truce called by most candidates during the crisis.

The killer, who died in a hail of bullets Thursday after trying to shoot his way out of a police raid, had a long criminal record and history of extremism and had been arrested in Afghanistan's Taliban heartland.

But Mohamed Merah was able to escape police surveillance, to assemble an arsenal of firearms and to carry out three broad daylight killing sprees at four-day intervals in the Toulouse region before he was caught.

"It seems Mr Merah had an almost caricatural profile as a suspect, a man with 15 criminal convictions, a man who twice went on training trips to Afghanistan and Pakistan," Le Pen declared scornfully.

Le Pen, who is trying to match her father Jean-Marie Le Pen's 2002 feat of winning through to May's second-round presidential run-off, accused the main candidates of dodging the issue of Islamic extremism.

Sarkozy responded from the presidential podium, announcing a raft of new laws to criminalise extremist indoctrination methods and training, but Le Pen was dismissive of what she branded the "mediocre" measures.

The president will nevertheless hope that the killings, which allowed him to take off his candidate hat and return to a role as head of state, uniting the nation, will boost his chances of re-election.

The need to calm tensions raised by the murder of Jewish children by a Muslim extremist has forced Sarkozy to tone down the divisive tone of his campaign, having previously declared France "has too many foreigners".

Even before Thursday's shootout, the latest surveys showed him closing with or even passing Hollande in first round voting intentions, even if the second round remains the Socialist's to lose.

Pollster Frederic Dabi of Ifop said it was too soon to know whether the shootings would reverse this logic and propel Sarkozy back into the Elysee, even if there are signs that he is beginning to win over Le Pen voters.

It remains possible, he said, that after the crisis has blown over voters would return to Hollande and his promise to ease Sarkozy's austerity measures. "No-one at this stage can tell which hypothesis will prevail."