The merger wasn't really that much of a surprise. The Carlists were basically fascists themselves as the Carlists at this time drew extensively from the "integral nationalism" of Action Francaise, which as we should know was largely derived from Sorelian revisionists who devised national syndicalism and laid the path for Italian Fascism. Many historians like Ernst Nolte and Zeev Sternhell recognize Charles Maurras and AF as the originators of fascism, predating the Italian fascists by about a decade and a half.
What has confused a lot of historians and armchair analysts is that national integralists repeated a lot of tripe about being the continuation of the old feudal reaction against the French Revolution, of course even in just their rhetoric they belied the falsity behind this claim. A common Francoist slogan was that Franco's Spain was "nothing more than the Spain of Ferdinand and Isabella", which taken at face value is absurd. Spain was a society of modern, industrial capitalism(although relatively undeveloped), not of manorialism and aristocratic lords and serfs. The Carlists made many such false claims too. Any claim of being a "traditionalist" in the context of opposing the enlightenment and the French Revolution while simultaneously supporting nationalism is paradoxical. Anyone who knows even the slightest about medieval history knows medieval society was characterized by intense regionalism, and nationalism mostly did not even exist yet alone exist as a prominent force.
The Spanish fascists of Primo de Rivera were very weak and inconsequential at our start date, but CEDA had a lot of facists in it, especially in the youth wing and the supporters of Gil Robles. In the election of February, 1936; the falangists polled at about 0.5% of the popular vote. Yet by the same time next year(before the merger!) they had over a million members and were the largest party in the whole country including the Republican Zone and the likes of PSOE. This is partially explained by the crypto-fascists who had previously been within CEDA defecting to the Falange, but that party's number is too gigantic to be explained by that alone. Clearly a lot of political radicalization was happening very quickly.
The people who planned the coup really had nothing to do with fascism. The plans for the coup were set in place in the beginning of January 1936 when the falange was still an inconsequential force. The generals leading the coup had a variety of ideological dispositions, but none at the start could really be considered fascist.
I would disagree strongly with the poster that Franco and the military "subdued" the fascists. On the opposite, I would say rather that Franco co-opted them and became the head of the fascists for some obvious reasons owing to their huge power and popularity. This all happened after the deaths of Sanjurjo and Mola in [separate] plane crashes.
In an ideal world, the Nationalists would start off as non-aligned with an option to become a democratic republic with Catholicism as the state religion, a democratic constitutional monarchy with Catholicism as the state religion, a more permanent junta which could perhaps involve restoring the Bourbon monarch and having a second kind of dictatorship similar to Miguel Primo de Rivera's dictatorship in the 20's, a fascist monarchy led by the Carlists, or the kind of compromise fascist state we historically got with Franco. That's what I would do at least, but from a plausibility perspective really only the last two were real options. The Junta came to rely extensively on the Carlist Requetes and the Falangist Blueshirts as auxiliaries and it was basically politically unthinkable for the junta to break from the fascists.
I think it would be pretty cool if Alfonso was only an option for France, and could only come to power in Spain through a violent conquest by the former. As others have said, Alfonso was pretty unpopular among pretty much everyone, even people sympathetic to the monarchy.
Great to see Spain coming. At the bare minimum it looks like we're getting a Carlist option in addition to a Franco one.