You can't really confine Fascism to the Left or the Right because Fascism was essentially a mixed economic system. It wasn't a static laissez-faire system or a static socialist system. Italian Fascism started as a syndicalist system, then transitioned to corporatism, then adopted economic liberalism (laissez-faire), then went back to corporatism, then abandoned that for socialism. The NSDAP also was a mix of socialist, corporatist and laissez-faire. The Strasser Socialists were purged entirely in 1934, so the NSDAP afterwards was corporatist, but strongly favored the laissez-faire economists and the industrialists because Hitler needed them to mobilize German industry for his war machine.

Both Nazi Germany and Fascist Italy had a "corporatist" economic system. It was a mix of capitalism and socialism where workers and capitalists managed the economy directly. Corporatism is actually common but Fascism was unique that it abolished Parliament and replaced it with representative mass labor unions and mass capitalist associations. In Social Democracies, the Corporatist unions/capitalists co-managed the economy with Parliament.

Rexford Tugwell and Hugh S. Johnson were admirers of Mussolini's Corporatist system. The New Deal, up until 1935, was a corporatist system but it was seen as an extension of Liberalism and Democracy. Tugwell and Johnson never intended to abolish Democracy. So although they replicated Italian Corporatism, American Corporatism was still a Liberal institution. Fascists acknowledged this distinction. Mussolini wrote a review of FDR's "Looking Forward" and actually praised his proposal for an economic Bill of Rights, but he also points out that these are all Liberal institutions aimed at preserving individual liberty, rather than a Fascist institution aimed at strengthening the State. The American Fascist Lawrence Dennis also points out that the New Deal was not Fascist because it was implemented as a short-term solution to the economic crisis. Dennis expected that the New Deal would be dissolved and the Supreme Court actually ruled corporatism unconstitutional in 1935.

It also needs to be pointed out that the political spectrum for Europe and America are different. In 1920's Europe, most governments were constitutional monarchies and the parliamentary democracies were censitary (landowners or Nobles got more votes). And male suffrage was not guaranteed (you either needed an education or property). On the European spectrum, Absolute Monarchy (no Parliament, the King alone rules) was the far-right, and socialism was the far-left. Economic Liberalism (laissez-faire) and Egalitarian Liberalism were near the center.

The Doctrine of Fascism defines Fascism as a right-wing system because it abolished Parliament and they mixed Absolutist Monarchism with Corporatism. Fascism was opposed to Liberalism entirely. It was opposed to both Economic Liberalism and Egalitarian Liberalism. Laissez-faire economics were not absolute.

In America, Monarchism was abolished entirely and replaced with a Constitutional, Democratic Republic. It was founded on Liberalism. Economic Liberalism was the far-right, and Egalitarian Liberalism was the left.

TL:DR; It used both Laissez-faire and Keynesian economics, but was opposed to both as ideologies. The State was absolute, but not it's economics.