Yabia: The Khazars lived in a Sefardic geographical area. Additionally, they were kosher Jews. In any event, the idea that they represent most of either Sephardim or Ashkenazim is an anti-Semitic idea. They were melted into wherever (Sephardim, Ashkenazim) as a tiny proportion.
The Ashkenazim came from Eretz Yisroel to France/Germany while the Sephardim came from Bavel to Spain/Portugal.