The "first generation" Jews who entered Europe were definitely "middle eastern looking".
But about 3 generations of intermarriage with native European is enough to diminish the "middle eastern look" of European Jews. Look at modern European Jews today, there's hardly any "middle eastern" physical traits left.
Take Bernie Sanders for example, would you be able to tell he's Jewish if you do not know anything about him at all?
And in reality the European Jews have been dwelling in Europe for centuries,