The quick and dirty definition of fascism:
fas·cism n.1. often Fascism
a. A system of government marked by centralization of authority under a dictator, stringent socioeconomic controls, suppression of the opposition through terror and censorship, and typically a policy of belligerent nationalism and racism.b. A political philosophy or movement based on or advocating such a system of government.
2. Oppressive, dictatorial control.
Source: The American Heritage® Dictionary of the English Language, Fourth Edition
Franco was and is universally recognized as having been a fascist.
Clearly Hitler and Mussolini considered him to be their fascist brother in arms.
The difference between Spanish fascism and that of Germany and Italy was the primacy of the party.
In Germany and Italy the state was subordinate to the party but it was vice versa in Spain.