No, it's in principle undetermined in ideology. Historical ones, even Stalin or Pol Pot variants, were rather right wing. But the only principles really important for any kind of fascism are violence, anti-rationalism and amorphous ideology.
EDIT: What I mean is that fascism is that "third way", not left-wing or right-wing. And has made situational alliances with things from both. That was its main difference from old conservatives in the beginning of XX century.