The nation of France remained on a state of alert last night, a day after three children and a rabbi were gunned down by a mysterious motorcyclist in Toulouse.

The gunman had already struck twice before, killing three black French soldiers in attacks on March 11, and March 15. In the first attack, Ibn-Ziaten was shot outside a gym in Toulouse, by someone who answered an ad for a motorbike he was selling.

In the second incident, Abel Chennouf and Mohamed Legouard were gunned down at an ATM, with a third man seriously wounded. In all these cases, and in the most recent shooting, the killer shot not merely at point-blank range, but with his gun held to the victims’ temples.

Witnesses reported that he appeared to have a small camera around his neck, to video the murders. Gunshot residue and the killer’s scooter caught on CCTV establish that it is the same killer.

Given the cold and efficient nature of the killings, and their spacing of four days apart, there seems little doubt that the killings are an act of social terror, although the earlier attacks were not immediately identified as a social/political act.

The attack on the Jewish children and the rabbi was initially seen as a separate act — raising the usual instant suspicions, though they were more muted in the mainstream than hitherto — until it was realised that the attacks were linked.

The killer remains at large, thousands of extra police are on the street, and there is a widespread official belief that he will strike again. Whether that belief will be borne out remains to be seen — it relies on the idea that the shooter is a compulsive serial killer, as most reports described him, who cannot restrain himself from killing.

That is certainly the version that President Nicolas Sarkozy wants to push. Currently campaigning in an election where he is running several points behind — campaigning was suspended by all parties for two days — he noted that the killer was a “monster — An anti-Semitic monster, but first of all a monster … Civilisation cannot guard us from the madness of certain men”.

“Serial killer”, “madman”, “anti-Semite” — throughout the past two days differing and contradictory accounts of the killings have circulated. When it was thought to be an attack on a Jewish school alone, it was marked out as a terror attack.

Linking with the two earlier attacks put it back in the serial killer category — the division between anti-Semitism and more general racism being one that is difficult to slot into an authorised political frame. Sarkozy fused it together in a form acceptable to mass-media sensibilities — a targeted killing, yes, but one without meaning.

Subsequently, multiple witness accounts of a camera around the killer’s neck emerged (though they may turn to be erroneous, and part media suggestion), which raised another possibility — that the killer was emulating Norwegian killer Anders Breivik, who had advised people conducting similar operations:

“[an] extremely small and lightweight field camera is used to document your operation,” Breivik noted in his “2083” manifesto. “4GB is equivalent to 2 hours of constant filming. I’ve personally tested it and it works great … Some governments may seize the movie (after you are neutralised) and publish it while others may bury it or even destroy it to protect the multiculturalist ideology.”

The mention of a camera raises the prospect that the killer’s actions are part of a series, by several individuals, responding to the same conditions in the same way — an obsessive race, or religious, hatred, justifying lethal force against the innocent.

The high-profile killings stretch from Breivik’s atrocity on Utoya island, to the recent killings of 16 Afghans by a marauding US soldier, to this most recent episode. They are connected not only by the nature of their target, but by the denial that there is connection or meaning to their acts. No sooner are they committed than they are put in the too-hard, i.e. “madness” basket, portrayed as acts with no core or content, or related to anything else in the world.

In France, Sarkozy’s desire to distance these atrocious acts from any conceivable content is all the more urgent, due to the o-gy of xenophobia in which his party has been engaging in recent weeks, in a desperate attempt to capture sufficient Front Nationale voters to retain his presidency.

Sarkozy and his cabinet have engaged in an o-gy of lunatic baiting over the past weeks and months — Sarkozy’s simple comment that there are “too many migrants in France” is the least of it. He’s also called for the labelling of all halal meat, so that non-Muslim people don’t accidentally eat it. Arno Klarsfeld, the new immigration chief, called for a wall to be built between Greece and Turkey to protect Europe from the barbarians.

But the most revealing remark was by prime minister Francois Fillon, also of Sarkozy’s party, who said that Muslims and Jews should abandon their religious dietary taboos, and become part of republican modernity.

Quite aside from revealing the totalitarian core of simplistic notions of “the enlightenment” — a hatred of any particularity or difference — it demonstrates something about the anti-Islamic chauvinism that the European Right have been trading in for so long.

For some time it has been clear that Islamophobia is a contemporary form of anti-Jewish prejudice (which, confusingly, is known by the general term “anti-Semitism”). But now there has been an inevitable knock-on effect connecting up with anti-Jewish prejudice.

Given the similarity of Islamic and Jewish taboos and observances — which sets both religions together, and distinguishes them from Christianity — there has also been the revival of Orthodox and ultra-Orthodox Judaism, whose followers look increasingly similar to Islamist Muslims. It was inevitable that their distinct practices would come under its sway.

That is what makes the Toulouse killer so hard to identify. Does his hatred come from the old hard Right, which was  anti-Jewish, anti-Islamic, and racist — a unity sundered by the new hard Right, which became assertively pro-Zionist and hysterically Islamophobic? Or does this killer represent a new stage, taken on by an extreme but lethal fringe — one in which difference is targeted indiscriminately from eight-year-old Jewish schoolgirls to black men in a paratrooper’s uniform? The Right has played with prejudice, and now a violent xenophobia is off the leash, armed with its manifestos, its obscuring helmets and its necklace massacre cams.