Four Jewish men, suspected of being members of the Paris branch of the Jewish Defence League, are in police custody, accused of vandalising a bookshop.
The JDL has links with the extreme-right Kach movement, founded in New York by Rabbi Meir Kahane in the 1970s.
It is outlawed by the European Union, Israel, Canada and the United States. It is also connected to offshoot Kahane Chai (Kahane Lives).
The attack took place last Friday at the Resistance Bookshop in Paris’s seventeenth arrondissement. Owned by Olivia Zemor and Nicholas Shahshahani, the shop is known as a meeting place for anti-Zionist activists.
Jewish-born Ms Zemor is the founder of the pro-Palestinian CAPJPO (Coordination des Appels pour une Paix Juste au Proche-Orient or the Organisation for Peace and Justice in the Middle East) and stood alongside the comedian Dieudonné in the 2004 EU elections for the EuroPalestine Party.
Books were ripped off shelves and doused in oil and computers were smashed.
After the attack, Mr Shahshahani claimed that the JDL — whose 200 members are mostly young Jewish men under 30 — is the “violent side of the Zionist organisation in France, the CRIF, which uses them for intimidation and protection”.
This was vehemently denied by Meir Habib, the head of the CRIF — the French equivalent of the Board of Deputies — who called the attack a “criminal act”.
He added: “We live in a democratic country in which anyone can express their opinion and sell books, even if they are anti-Israel.”
Meanwhile, the JDL’s French website put out a press release saying that “the JDL denies any connection with the attack at the Resistance Bookshop”. It goes on to demand that CAPJPO be outlawed.
The JDL in France, called the LDJ (League de Défense Juive), is not an illegal organisation, but is regarded by the majority of the community in France as a group of extreme rightwing troublemakers.
Although very much a minority, its members are usually present at anti-racist rallies and demonstrations in the French capital, and their activities frequently degenerate into acts of violence.
In 2008, it provoked the anger of the organised community after sabotaging an event organised by CRIF in honour of Israeli President Shimon Peres.
However, communal officials have also admitted that the JDL has occasionally assisted in the battle against antisemitism, informing on anti-Jewish groups or websites that they monitor.