I cannot speak to Portugal, but I have a note on the premise of your question: we have to be careful in ascribing the "fascist" label to Franco's regime. In no way is this exculpatory, because Franco's regime was murderous from the very beginning. "Barbarous" is the word used by historian Jose M. Sanchez, and I think that is apt. However, fascists and fascism made up only a part of Franco's support and his regime. For instance, in the 1936 Spanish Elections the fascist party got less than 0.1% of the votes (look for Falange Española de las J.O.N.S. in the election results here. That's less than 7,000 votes out of over 9,000,000 cast. That's not to say that there weren't people who leaned towards the Falange in other rightist parties, but the outright support for fascism within rightist Spain was anything but absolute.

Franco's Nationalists were made up of the military, large industrial and agricultural concerns, two separate (and mutually antagonistic) monarchist groups, the remains of the Catholic center party (CEDA), and other interests. A distressing number of the Catholic hierarchy also supported Franco's revolt. But to ascribe the "fascist" label to Franco is problematic. There were certainly fascist aspects to the Nationalists and Franco's government, but Franco's main cause wasn't fascism--it was Franco. He had an uncanny ability to subsume other causes to his own. Each group of his supporters was played off the others and manipulated into putting Franco in control. His rivals for power were sidelined or died quite conveniently (such as generals Sanjurjo and Mola). That fate also befell the leader of the Falange, Jose Antonio Primo de Rivera. He was imprisoned in Madrid before the war began and was executed during the war. His organization--like the rest of Franco's supporters--was absorbed into Franco's overall apparatus and merged with the monarchist groups into the single Nationalist party.

Franco's support for traditional power structures makes him a poor fit for most of the definitions of a fascist. He was a military man and was dedicated to that conception of himself, and he backed this traditional form of power. He also gave varying degrees of support (from lip service to actual backing) to the concept of monarchy, traditional landed elites as well as industrialists, and the Catholic Church. Other than the military, none of these groups got unqualified support. However, Franco's efforts to embrace these traditional groups makes him a poor fit for most of the standard definitions of fascism.