Some say Franco wasn't too ideological. A conservative authoritarian and a pragmatist, who united the anti-Communist factions -- Falangist, Carlist, Monarchist, etc. -- to fight the Reds.
Franco himself wasn’t a Fascist. He was a Catholic traditionalist. The Fascists were revolutionaries. Franco’s government, however, was partially Fascist from 1936 to 1944 because some of the ministers belonged to the Falange, which was a Fascist group. Franco had Falangist ministers because during the Civil War he needed Italian and German support and later - during WWII - he didn’t want Spain to be attacked by the Germans. After 1944 the Falange lost all influence and was only kept for ceremonial purposes.
I recommend reading some books by Stanley Payne, a non-leftist historian who wrote extensively on Spain and Fascism.
There were Jewish Fascists in Italy Musolini disliked the Nazis Antisemitism, but then he started to kiss up to hitler.