Bernheim, 60, submitted his resignation and apologies at an emergency leadership meeting of the Central Consistory, the top Jewish religious authority, after initially trying to hold on to his post despite acknowledging his faults.
Video courtesy of jn1.tv
In a statement, Bernheim said he quit because it was "no longer possible to fulfill (my) duties with the necessary serenity and tranquility" and hoped the controversy would not overshadow his years of service to French Judaism.
Until the scandal broke last month, the modern Orthodox rabbi was better known as a leading religious commentator on public affairs, including increasing anti-Semitism in France, and an active participant in interfaith dialogue.
His recent booklet opposing a government plan to legalize same-sex marriage this year won unexpected praise last December from former Pope Benedict, who called it a "very detailed and profoundly moving study" defending traditional matrimony.
In its statement, the Central Consistory's Council "took note, with emotion and sadness, of the decision of the chief rabbi to resign" and said his "authority and spiritual contributions are considerable."
CRIF, the umbrella group of Jewish organizations, said Bernheim had given French Judaism "an image of conceptual rigor and openness to public life."
Central Consistory President Joel Mergui described the plagiarism scandal as a "grave crisis" for France's 600,000-strong Jewish community, the largest in Europe, and said an election for a new chief rabbi would be held in a few months.
Bernheim's fall from grace followed recent resignations in Germany, where Chancellor Angela Merkel's defense and education ministers were found to have copied parts of their doctoral theses, and the resignation of an Italian anti-corruption politician claiming academic degrees he did not have.
Bernheim initially denied plagiarism when accused last month of copying a text by the late post-modernist philosopher Jean-Francois Lyotard for his 2011 book "Forty Jewish Meditations."
He later admitted it was copied but blamed it on a research assistant.
Another blogger then accused him of plagiarism in a 2002 book and L'Express magazine revealed he was not the philosophy professor he was often described as being.
Although his official biography did not mention him passing the "agregation," the highly selective examination needed to qualify as a professor, Bernheim never disputed the title when it appeared in newspaper articles and publicity for his books.
Confronted on Radio Shalom on Tuesday, Bernheim spoke of "loans which others will call plagiarisms" and admitted never denying the academic title others attributed to him.
These moral failures were not enough to justify stepping down, he said. This sparked a flurry of comments for and against him on social media and his spokesman quit without giving any reason.
"It's clear a lot of people are upset and disappointed ... but they are also thinking about the pain and state of turmoil he finds himself in," CRIF President Richard Prasquier said.
Ashkenazi and Sephardic
Bernheim was a leading proponent of a more modern and open Judaism when he challenged incumbent Joseph Sitruk in a hard-fought 2008 race that revealed deep splits in French Judaism.
Although both were Orthodox, Tunis-born Sitruk was a popular traditionalist who represented the Sephardic Jews who emigrated from North Africa in the 1950s and 1960s.
Bernheim, who grew up near the Alps, comes from the long-established Ashkenazi community of East European Jews that had traditionally led French Judaism.
A book he published with Lyon Cardinal Philippe Barbarin before the election prompted some critics to accuse him of being too close to France's Roman Catholic majority.
The election campaign became so divisive that two major Jewish organizations and the Catholic priest in charge of relations with Jews appealed to both sides for calm.