Police sources are reported as saying the same gun and stolen motorcycle were used in all three attacks.
The school shooting, described by the French president Nicolas Sarkozy as a "national tragedy", raised fears that a killer driven by hatred of ethnic minorities is at large.
Among yesterday's dead were a teacher at the Ozar Hatorah school in Toulouse and his two sons, aged six and three. The third child to die was the headmaster's 10-year-old daughter, and a 17-year-old boy while critically injured.
Their deaths follow the killings of three soldiers belonging to airborne regiments last week. All were of African Maghrebin origin while a fourth paratrooper, seriously injured in one of the attacks, is black and from the French Caribbean island of Martinique.
The Toulouse public prosecutor, Michel Valet, said a link between all three shootings was possible, while Agence France-Presse quoted a police source close to the inquiry as saying ballistics experts found the same .45-calibre automatic pistol, and the same motorcycle, were used.
Mr Valet said the gunman used two weapons in the school shooting. A 9mm pistol jammed and he began firing with the other gun.
"He shot at everyone he could see, whether children or adults, and some children were chased into the school," he said.
The killer struck at about 8am local time at the drop-off point for parents of children of nursery and primary-age.
As in the previous shootings - two soldiers were shot dead on Montauban last Thursday and one in Toulouse, 46 kilometres away, four days earlier - the gunman rode up on a powerful motorcycle.
He was dressed in black motorbike leathers with his helmet visor pulled down over his face, although one witness to the Montauban shooting has said it was raised as he passed her, showing him to have a facial tattoo.
If it is confirmed that the same gunman carried out the three attacks, with or without accomplices, it widens the possible motives.
There was widespread speculation last week that the soldiers, whose units have served in Afghanistan, were shot by someone violently opposed to France's military involvement against the Taliban.
Although the possibility of a killer without coherent political objectives cannot be excluded, it is now at least as likely that a grudge against minorities or foreigners is behind the killings.
The adult who died yesterday was Yonatan Sandler, a Franco-Israeli teacher of religious studies, his sons, Aryeh and Gavriel, and Miriam, the daughter of the headmaster, Yaacov Monsonego.
One pupil's mother, who lives nearby and witnessed the shooting, said she felt "terrorised", adding: "I saw children running off. My view was partly obstructed by the gate, but I saw feet lying on the ground. Then the gunman came out on the pavement outside my house. And then he shot again at the people closest to him, almost at point blank range."
Mr Sarkozy, who went immediately to the scene, said a minute's silence would be held in all French schools today.
Describing the shooting as an act of "savagery and cruelty, he said: "On the territory of this republic, no one assassinates children like that without being brought to justice."
Gilles Bernheim, the chief rabbi of France, also travelled to Toulouse. 'I am horrified by what happened … It has bruised by body and my soul," he said.
Politicians suspended campaigning in the presidential elections to be held on April 22 and May 6. In Paris, prosecutors opened three separate murder inquiries.
Security is to be tightened at schools, synagogues and other establishments linked to France's Jewish community. Similar steps are being taken in neighbouring countries, such as Belgium.
Pierre-Henri Brandet, spokesman for the French interior ministry, ordered police throughout France, but particularly in the southwest, to "strengthen surveillance and vigilance around places of Jewish education".
Chief Rabbi Pinchas Goldschmidt, the president of the Conference of European Rabbis, said: "This horrific act is indicative of a society where intolerance is allowed to fester. We call upon the French authorities to take all steps to ensure that the perpetrator of this act is found and brought to justice."
The shootings of the three paratroopers, also in daylight, had already prompted the French media to talk about a "race against time" to catch the killer or killers.
The targeting of small children added a sinister new dimension to the investigation, but it was not the first time a Jewish school has been attacked in France. In 1995, 14 people were hurt when a car bomb exploded outside a Jewish school in a suburb of Lyon. The blast occurred shortly before 700 children were to leave school.
Thirteen years earlier, six people were killed in a grenade and gun attack in the Marais, traditionally a Jewish quarter of Paris. There have also been frequent vandalism attacks on mosques.
Toulouse has one of highest numbers of Jews in France, though the estimated national total of about 500,000 is much smaller than France's Muslim community, put at five to seven million.