I think you know me well enough to believe me when I say that I'm not really one of those people who pick one side in a political debate and then stick with it no matter what, and that I can be critical of those on my "own side" when necessary. Not that I would even describe myself as being particularly on the Palestinian side; if it ever did come down to being forced to pick one side or the other, it's more likely that I'd choose Israel. Fortunately, that kind of black or white choice isn't required, and people can have more nuanced views, finding the nutcases and fanatics on both sides equally repellent.

If I agree for a minute to generalize and talk about "Europe" as a single entity, then I'd say Europe neither loves the Palestinians nor disdains the Jews. Believe it or not, but the Holocaust has in fact wiped out the persistent anti-Semitism that existed even in parts of the mainstream in pre-war Western Europe; and the growing Islamic presence in Europe in recent decades has considerably reduced it even on the far-right where it had survived (I wouldn't really say that's to their credit, though, it's more an "enemy of my enemy is my friend" deal in that last case). In East-Europe it's still somewhat more present in some countries, that's true (but those countries aren't usually very vocal on the topic of Israel, that I've noticed).

"Europe" does however have a preference for the underdog in any conflict, especially in conflicts that look colonial in nature (i.e., where a European community is locked in a struggle with a non-Western people), due to a lingering sense of guilt over its colonial past. That is really at the heart of it. The sympathies of the Europeans started to shift pretty much around the time that the balance of power in the region shifted decisively in Israel's favour - the wars of 1967 and 1973. And if somehow Israel suddenly found itself on the losing end of the conflict, it would find that it has far more friends in Europe than it may think.

Lastly, I want to add just one thing about your "two thousand years" remark. Last I checked, the ancestors of the large majority of Americans have been European for all but the last one to three centuries of those two thousand years, four at most. It's fair enough for Americans to criticize the modern European anti-semitism of the nineteenth and twentieth centuries, but as for the medieval kind, you're responsible for that as much as any European is.