France emancipated Jews at the Revolution and gave them equal rights, which attracted many from the rest of Europe and allowed them to climb the social ladder very well thanks to the meritocratic education system. But that's also what caused antisemitism to get so big in France: the Catholic far-right came to blame the Revolution on a Judeo-Masonic conspiracy, and the success of Jews in the new regime bred a lot of jealousy. It only got worse after 1870 when Adolphe Crémieux, a (Jewish) minister in the non-elected interim government of national defense, decreted that all Algerian Jews would automatically become citizens (but not the Muslims or the European immigrants). This ultimately turned to be a pretty good decision given (and it was a good first step in the goal of the time, which was assimilation of Algeria into France), but it caused a huge outrage because of the obvious favoritism. A guy named Drumont, who was pathologically obsessed with Jews, created his own antisemitic newspapers and political party, and he had a huge influence on the political landscape, especially on the conservatives but not only (many socialist antisemites). For the entire period, government was systematically controled by the Radical-Republicans, who stayed loyal to the ideals of the Revolution, while the army remained mostly royalist, conservative and antisemitic. That's the root of the Dreyfus affair, but it didn't stop there at all, because every victory against antisemitism could be interpreted by the far-right as further proof of Jewish control over the government. Things heated up a lot in 1936, when the far-right attempted a coup; it failed and in reaction the Popular Front was elected, led by a Jewish socialist. After 1945, as in most of Europe antisemitism was completely discredited, but in France on top of that it became associated with treason. Jean-Marie Le Pen kept baiting the old antisemites by making well calculated remarks, but all this has mostly died out.

The antisemitic wave that we see now doesn't stem from all this history, but almost entirely from the young Arab / Muslim population, and essentially based on the Israelo-Palestinian conflict.