Fascism is hard to define on a right-left scale. It is socially authoritarian and has mixed economic views which could be described as 'the government cooperating with and coopting major corporations', which is neither left (Government bossing businesses around or replacing them) or right (Government leaving businesses alone or being coopted by business); it contains elements of both. "Corporatism", much as some supposed right-wingers might favor it, cuts both ways.
Technically, Franco was a Falangist, not a Fascist. Falangists were more closely connected with Christianity, in the case of Spain Catholicism. Neither was/is a racist ideology (although both are staunchly nationalist). Another form of Falangism is the Kataeb movement in Lebanon, they're the major 'radical Christians' who are diehard enemies of Hezbollah and other such groups. Kataeb has received backing from Israel, among others.
National Socialism is not only not quite fascist but it also had right and left wings. Rohm represented the hostile-to-business left wing; Hitler toyed with both and eventually favored the right in order to garner favor from 'anti-communist' types. Plus, remember that "NSDAP" is German for "National Socialist German Worker's Party", and was originally leftish but veered right to become a more viable anti-communist movement. Unlike standard fascism, Nazism is racist and combines race ("Aryans") with the nation ("Greater Germany"). Nazism also contains a somewhat anti-clerical element; some more radical Nazis even favored Odin and the other Norse gods over Christianity, especially Catholicism. This is opposed to Falangist's close association with Christianity, indeed it is opposed to the more clerical wing of Italian Fascism. I'd call Nazism in its complete form more of 'Hitler's wet dream ideology writ large' than anything else, right left or center.
Actually, a true 'pure' right or left government is an impossibility anyway. There's no way you can restrict all of one type of liberty (Economic or social) without some restrictions on the other. Communism is a left-dictatorial system but it isn't 'pure' by any means as it contains social restrictions. Likewise, any pure right-wing ideology would be impossible; no theocratic state could offer a pure lasseiz-faire capitalism.