In any case regardless of their genetics, Askenazi Jews are European because:

1. They basically do come from Europe (in the geographic sense of where they really became a people different from other Jews complete with their own High German language)
2. In the first approximation they think of themselves and others think of them as European-derived/White or at the very least Western nearly anywhere in the world they live in (be it France, South Africa, the US or even, rather interestingly, in Israel).
3. Extensive memeplex exchange with the Christian peoples of Europe.
4. High rates of intermarriage in the 20th and 19th century.

If history had gone a bit differently and there was a Yiddish speaking Askenazi state somewhere near Poland/Ukraine/Belorussia, geneticists would say that its an interesting example of a Eastern European population being genetically closer to Souther Europeans than their neighbours but wouldn't really break them out as "genetically non-European" as say some Roma populations are.

Of course Askenazi identity is now somewhat tied to Israel which is a homeland for all Jews. But even if this evolves into a true new Jewish Middle Eastern identity, these are still quibbles about geography, religion (quick question do you think Turks would have ever been considered non-European had they been predominantly Christian?) and culture that have little to do with the genetic reality (though those things do correlate in many circumstances).