I think what you say is true, but somehow does not tell the whole story. And each has its own and very different, and very complicated, roots.
Antisemitism means hostility towards, or suspicion of Jews, on a racial rather than religious basis. It does not belong only to the political right, but can belong to the centre and the left.
Islamophobia means "fear of Islam." And Islam is not just Arabs, it is in Pakistan, Turkey, Iran, Indonesia, Africa, etc.
If I pretend to be an average French citizen:
I might be hostile to Jews because I think they overcharge me at the local shop, or because they are not Christians like other "real" French people, or because I believe they control the world's financial systems. But I do not "fear" them.
But, after the Bataclan massacre, the Charlie Hebdo massacre, the lorries driven into crowds and a dozen other acts of violence in the name of Islam, I do "fear" Islam. I see Islam as an invasive and direct threat to my average, familiar middle class French world.
So, what do I do? I vote for Le Pen.