Fascism is just populist extreme conservatism (Franco!). The Republican party is far from populist.
Actually, contrary to popular belief, Franco wasn't a fascist. He was a far-right authoritarian who enjoyed the support of many traditional institutions, whereas genuine fascists like Mussolini and Hitler held far more revolutionary beliefs and frequently criticized said traditional institutions.
While being backed by other conservative institutions. Franco was a fascist. Yes, he was.
Franco was a fascist who "won", if you like. He didn't get violently kicked out like Mussolini or kill himself to prevent getting violently kicked out like Hitler. The sweeping changes in Spain took place after he died and Juan Carlos (to whom Franco had given the title Prince of Spain rather than the traditional Prince of Asturias, possibly to emphasize that Juan Carlos was succeeding because Franco said he was and not because he had any right to the throne--Juan Carlos's claim wasn't the strongest, but his dad was an outspoken critic of Franco) became king. At that point, Juan Carlos told some people to write up a constitution and mostly got out of politics.