Ironic how you have blacks trying to prove they're Jews and Jews trying to prove they're Gentiles.
Looks like Shlomo Sand isn't even an expert in ancient history according to citations on that wiki article but rather a expert in European history.
The problem with his arguments is that they are rather "subjective" in that they support his theories based on populations converting but there were never mass conversions, while individual conversions did exist. His claim on the Khazars has been debunked numerous times, the only people who even claim of having ANY Khazar ancestry are the Crimean Jews in Ukraine who speak a Turkic language.
Some of the North Africans did convert to Judaism, a few Berbers but most of them mixed in with the Jewish population anyways just like Canaanite tribes mixed with Israelites. It's not even known if Kahina really converted to Judaism but it's rumored, there's no facts to back that.
As for Europe, I'm not aware of any point in time that any European population mass converted to Judaism, it was seen as a bad thing to convert to Judaism especially during the dark ages and there's no evidence of Khazars ever migrating into western Europe at any given point in time but it's well known that Southern Italians share similar genetics to the middle east which would support a migration theory.
Lets not forget Carthage either which was established by the Phoenicians, they sailed all over the Mediterranean and established colonies and it's been said Israelites/Jews were aboard those ships as well which would support migration theories.
Either way, I don't mind reading an enemies book just to debunk it and prove it wrong.
I find his book as historical as reading a Lord Of The Rings novel.