On Monday night, the respected news magazine Le Point said police were seeking three ex-paratroopers, from the same regiment as the Montauban victims, accused of having links to a neo-Nazi network.

The school massacre sparked widespread cries of sorrow and calls for action in France and beyond.

The Interior Ministry ordered police headquarters across the country to step up security around Jewish schools and colleges, because this act of terror identifies it’s self as an act of Antisemitism.

“The whole French republic is touched by this abominable drama,” Sarkozy said. “We must not give in to terror, to barbarism, to savagery; cruelty and hatred must not be allowed to win; the republic is much stronger than that.”

Mohammed Moussaoui, president of the French Muslim Council, said he was “horrified by this indescribable criminal act.”

The gunman at the school struck shortly after 8 a.m., killing Franco-Israeli rabbi Jonathan Sandler, who taught there, as well as his two young children and the girl.

Sandler arrived in Toulouse in September for a two-year post at the 200-pupil school. Israeli radio reported that his body and those of his sons will be flown back to Israel for burial.

Speaking after Monday’s shooting, local prosecutor Michel Valet said the gunman first used a 9-millimeter weapon, “firing at everything in front on him.” When that gun jammed, he switched to the heavier weapon, shooting inside the school before fleeing on his motorbike.

“He shot at everything he could see, children and adults. Some children were chased into the school,” Valet 

Last week, witnesses described how the Montauban killer stopped to calmly turn over one of the soldiers who was trying to crawl away into a nearby shop and fired three more bullets into him before jumping back on his vehicle to escape.