No one was killed or injured in the attack on Sunday, but an unpublished website statement from an unknown Islamist group which claimed responsibility for the attack is being treated with scepticism.
French officials said they would not completely rule out Jamaat Ansar al-Jihad al-Islamiya in their investigations.
"But this is not what we were expecting. We are thinking about a more national, more local lead," a magistrate said. "This would not be an emblematic target for an Islamist group based in Dubai or in Egypt.
"What makes us think about a national lead is the fact that not everyone in the world knows the Rue Popincourt, nor this small social centre, which is not a synagogue," he added.
Tel Aviv said Foreign Minister Silvan Shalom would make what it called a "solidarity visit" to Paris on Tuesday, after two high profile attacks on Jews and their property.
He is to meet French Foreign Minister Michel Barnier, it said.
France and Israel clashed last month after Israeli Prime Minister Ariel Sharon urged French Jews to emigrate to Israel to escape the "wildest anti-Semitism".
The Israeli foreign minister is to
meet his French counterpart
French Prime Minister Jean-Pierre Raffarin said those guilty could face up to 20 years in prison or even life sentences under a new anti-racism measure in France, home to western Europe's largest Muslim and Jewish minorities
A number of racist attacks have hit eastern France, with more than 300 tombs or graves desecrated since April - many in Jewish cemeteries and also some Muslim and Christian graves.
Paris's Mayor Bertrand Delanoe said on Monday extra funds would be made available to help make Jewish property safer. Information panels would also display anti-racist messages, he said.
But it is not only Jews who have been targeted. In a recent attack in Strasbourg on Saturday, a swastika was found scribbled on the office of the wife of Abd Al-Haqq Nabaui, the head of the region's Muslim council.
The desecration of Muslim graves in Strasbourg in June prompted French President Jacques Chirac to announce a new drive to end ethnic intolerance in France.