News of the possible ban on the Jewish Defence League (LDJ) came just ahead of a Thursday evening pro-Israel demonstration to be held outside the Jewish state's embassy, located near the French prime minister's office.
The rally called by the Representative Council of Jewish Institutions in France (CRIF) is in response to weeks of protests marred by clashes, arrests and allegations of anti-Semitism in which synagogues were targeted and Israeli flags burnt.
The CRIF's head Roger Cukierman distanced his group from the LDJ as news of the possible ban emerged, saying: "We share neither their ideology nor their methods."
"It's a tiny organisation comprising a few dozen members from what I know," he said, but expressed surprise that the government was not planning to ban "pro-Palestinian groups which have tried to vandalise eight synagogues in the Paris region."
The presence of charged-up JDL activists on the sidelines of recent rallies was seen as one of the reasons they turned violent, with clashes outside a synagogue on July 13 leading to a ban on subsequent pro-Palestinian protests.
"We are carrying out an extremely fine analysis of the law," a source close to the case told AFP, confirming a report by French newspaper Liberation of the move to disband the LDJ.
Last week Interior Minister Bernard Cazeneuve said the group's actions were "excessive" and "should be condemned".
The French LDJ denies breaking French laws. It takes inspiration however from the far-right Jewish Defense League, labelled a "violent extremist organization" by the FBI in 2001.
It also uses the emblem of a banned Israeli far-right party, the Kach, a raised fist inside a black Star of David, set against a yellow backing.
Here's a video of the violence near the Paris synagogue:
The Gaza conflict has stirred up huge passions in France — home to the largest Muslim and Jewish communities in western Europe with around five million Muslims and half a million Jews.
While many protests around the country have gone smoothly, some demonstrations in Paris and the northern suburb town of Sarcelles have descended into chaos and looting in which Jewish businesses were targeted.
French far-left and Muslim leaders have been calling for action against the LDJ, with the French Muslim council branding it "an extremist, racist and violent association."
The government meanwhile has come under attack for banning some demonstrations on the ground that it went against the principle of freedom of speech and assembly.
Far-right leader Marine Le Pen meanwhile blasted the ruling Socialists for failing to stem "riots in the heart of Paris" after having banned demonstrations.
"We must protect the right to demonstrate but from the moment that the state takes a decision to ban a rally they must provide the powers so that the ban is respected," said the head of National Front party.
"We ask policemen to confine troublemakers within a specific perimetre but… neither to arrest them nor to burn or break everything," she said Thursday.
Scores of people have been arrested following the riots and unrest that marked most of the Gaza demonstrations in and around Paris.