The Jews have been both central and instrumental to the polarization of French society. The 20th Century started with the Dreyfus affair. Dreyfus was a Jewish army officer who was falsely accused of espionage for Germany. Even though it was realized that the charge was not only not supported by evidence but untrue, the army went ahead with the court martial rather than face the embarrassment of withdrawing the charge. Dreyfus was sent to Devil's Island in Guiana for life. Like Watergate the case began to unravel and in the end Dreyfus was exonerated. In the course of it the novelist Emile Zola wrote "J'Accuse" which implicated everyone in power up to and including the premier.
It was a crisis for France and a trauma for the Jews. It split France into two factions, the Dreyfusards and the anti-Dreyfusards. The issues between them were by no means limited to Dreyfus. The Dreyfusards stood for liberalism, tolerance, freedoms of speech and press, separation of church and state, and so on. The anti-Dreyfusards were the right, the peasants, the army, the church and the religious, the upper classes. The divisions either created or revealed by the Dreyfus affair persisted for generations. For example, Accion Francaise, the French fascist party, specifically arose from the anti-Dreyfusards.
In 1936 the Popular Front, a collection of leftist parties, won the elections and elected the head of the Socialist Party, Leon Blum, Premier. Under the Third Republic the Premier had far more power than now under the Fifth Republic and was much more like the British Prime Minister. Reactionary anti-Semitic anti-Dreyfusard military officers like Petain were aghast that a Jew should rule France. It is not polite to mention that DeGaulle sat on the same general staff as Petain and his opinions were almost certainly no different. One should not mention that fact to anyone of French nationality under any circumstances, no matter how friendly or well-disposed.
When the Vichy regime was established under Nazi oversight, anti-Dreyfusards like Petain saw it as an opportunity to get even for the slights and indignities they had suffered under Dreyfusard rule, and having had progressive Dreyfusard policies shoved down their throats for a generation. Because of the conglomerate origin of the anti-Dreyfusards, anti-Semitism was a unifying policy for the right. Vichy consistently cooperated with the Nazis in arresting and deporting Jews to German death camps.
The French Jews were the most assimilated in Europe in 1900. They believed that anti-Semitism was a waning relic of the middle ages like feudalism, superstition, religious fanaticism, serfdom, ignorance, and illiteracy. This was not mindless reactionary Tsarist Russia which had only just freed its serfs, but liberal enlightened republican France. If widespread anti-Semitism appeared here, a century after the Revolution of Liberte, Egalite, Fraternite, then the "waning medieval relic" theory was wrong. If Jews were not safe in France, where could they be safe?
Among the journalists sent to cover the Dreyfus affair was a young Viennese Jew named Theodore Herzl. In reaction to what he saw in France (and also in Vienna) he wrote a book called "Die Judenstaat". It is generally regarded as the founding document of the Zionist movement. Israel was founded not only because the Jews were not safe in Russia and Poland, but also because they were not safe in France.
The shock of Jews being arrested and turned over to the Nazis by French police acting on orders of the French government has never gone away. There is a plaque on every elementary school in Paris commemorating the arrest and deportation of Jewish children by French police acting on behalf of the French state. Those plaques started being put up in 2004, sixty years after the fact. That delay is significant in that it shows not only the resistance of the French to acknowledging what they did, but also to their delaying until no one could be held to account for it. The plaques give a Gallic shrug to accountability.
Under the Fourth Republic, which had a large Dreyfusard influence, relations between France and Israel were excellent. Both countries had suffered under the Nazis and after 1954 both were at war with the Arabs, the French in Algeria, the Jews on all fronts. The famous victory in the Six Day War of 1967 was won with French-built Mirage fighter planes.
Then came DeGaulle and the Fifth Republic. DeGaulle made anti-semitic remarks in public (the infamous "stiff-necked domineering people" remark) and began a rapprochement with both the Arabs and the Soviets. Israel turned to the United States for both support and arms. The Gaullists have continued that policy to this day.
I do not know enough about France to say whether the Dreyfusard - Anti-Dreyfusard dichotomy could be said to still exist as more than a metaphor. But there is certainly no moment of discontinuity when one could say it died. The legacy of DeGaulle in the ruling Gaullist parties certainly suggests that it is not gone.
My impression is that few French Jews live outside big cities, particularly Paris. French Jews are even less observant than American Jews but are somewhat less assimilated. Those who are observant are more observant than their American counterparts. There is substantially no French equivalent of the American Reform and Conservative movements. What little there is consists of American ex-pats and their French spouses. It is my impression that many or even most of the small pret-a-porter distributors on rue Saint Denis and around Place de la Republique and rue du Temple are owned by Jews. None of the big haute couture places in the Seventh seem to be.
I should add that when I was in Paris in 1977 I was told that the overt anti-semitism encountered by French Jews came not from the Arabs but from the French. Whether that is still true I do not know.