The text will be presented to the European parliament on Monday. It calls on Prime Minister Benjamin Netanyahu's government to halt Jewish settlement building on the occupied West Bank and in Arab districts of east Jerusalem.
"Systematic support of Israeli government policy is dangerous and does not serve the true interests of the state of Israel," says the text, available in six languages on the website www.JCall.eu.
"Our objective is to create a European movement that will allow the voice of reason to be heard by all," it adds.
"This movement is non-partisan. Its aim is to ensure the survival of Israel as a Jewish and democratic state. This depends on the creation of a viable and sovereign Palestinian state."
While many signatories have a history of strong support for the state of Israel, the main Jewish groups in France -- home to Europe's biggest Jewish population -- reacted with anger.
"This will largely be used by those who are true enemies of Israel," warned Richard Prasquier, chairman of the Jewish Representative Committee of France, one of the community's main representative body.
"It's very serious because these are prestigious personalities," he added, saying that Levy and Finkielkraut had made a "serious mistake".
Joel Mergui, president of France's Central Consistory, called the wording of the petition "excessive" and said he was "shocked by the term 'a call to reason' when Israel is a democratic state."
The chairman of the United Jewish Social Fund, Pierre Besnainou, said he was worried about "Jews being divided in public" and Claude Barouch, deputy head of the Jewish employers' association, said the call "weakened Israel".
These groups have launched a counter petition that by late Friday already had slightly more signatures than JCall.
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