Fascism is an extremist form of government that combines strict economic socialism, authoritarian single party government, and fervent nationalism. It is a dichotomy of extremes and gained ground as a political force starting around 1913 in a response to bourgeois capitalism.
The party was created to draw workers away from communism and into völkisch nationalism. Initially, Nazi political strategy focused on anti-big business, anti-bourgeois, and anti-capitalist rhetoric, although this was later downplayed to gain the support of business leaders working under government oversight, and in the 1930s the party's main focus shifted to anti-Semitic and anti-Marxist themes.
Although the economic and governmental structure of the Nazi party mirrored far left ideology, the National German Socialist Workers Party is generally considered a far right party because of its fervent Nationalism and authoritarian civic structures.
Well, at least you recognize that the fascist movement has always been diametrically opposed to Marxism to the point of imprisoning and killing Marxists alongside homosexuals, gypsies, and Jews. However, fascist economics never looked anything like far left ideology. Fascist economics is predicated, first and foremost, on the buildup of the military. Seeing as how leftists around the world decry militarization, that's a mark against any similarities. Fascists also oversaw mass privatization of their economies, again, a mark against similarities. And Fascists cracked down on unions in order to give corporations unlimited power over the working conditions in their workplaces, another mark against similarities. The only real similarity is that both communist and fascist government exerted control over the economy (and I'd like to point out here that Soviet-associated nations are not the only governments that can be considered far-left, so this can't be universalized to all leftists). However, where the Soviets generally assumed direct state control over many businesses, fascists preferred to set up a system where business leaders had direct access to the government and enjoyed benefits from this access in exchange for compliance. If all of that mirrors any economic ideology very closely, it's modern Republican ideology.