I would argue that he was not. I think for Franco, fascism was a scam. A way to get military aid from Mussolini and Hitler. He was more of a caudillo - a military dictator.
Franco's first cabinet, after the end of the civil war, had only two members of the Felange, the fascist party. Fascism, real fascism as opposed to "I disagree with you so you are a fascist" fascism, is anti-clerical but Franco supported the church. When he died, he willed leadership of the country to King Juan Carlos, not to the the leaders of the Felange. (Juan Carlos promptly declared a constitutional monarchy, put a parliament in place and assumed ceremonial duties.)
Under Franco Spain's economic system was arguably fascist - state control of education, natural monopolies and the means of propaganda but there wasn't a great emphasis placed on the regulation of industries or monopolization except maybe in the arms and aerospace industries.