First, it's worth considering what exactly is meant by fascism and who counts as a "true ideological fascist," which is far from a straightforward answer. If you want to read more on that, this post has a lot of answers and discussion. I am personally fond of Umberto Eco's wonderfully written essay Ur-Fascism, which discusses some of the difficulties involved in defining fascism and gives a set of 14 different characteristics which Eco sees as allowing fascism to coalesce around. They're not all always present and no single one of them is required to have fascism. However, I imagine that Eco's definition is probably far broader than what you are looking for and thinking about in terms of whether Franco himself was personally a fascist.
So are we any closer to answering the first part of your question? As it turns out, not really: There is no total academic consensus on whether Franco was a fascist or not, as /u/crrpit discusses in his answer here. There are some further points for consideration and references to more sources to look at if that's your thing in this answer by /u/special-case-8020.
To your question about co-option, as the latter answer points out, Franco made a point of subjugating and merging the myriad political factions in the Nationalist camp in the civil war into the Falangist FE de las JONS, which was renamed the FET y de las JONS (the added T standing for "traditionalist," which is conveniently enough the key issue in classing Francoist Spain as fascist). It is worth noting that the main Spanish fascist leader and founder of the FE de las JONS, José Antonio Primo de Rivera, was arrested by the Republican government a few months before the right-wing coup attempt that started the civil war, and was executed later in 1936. There are rumors (unsure how true they are, but that they exist is telling) that the Republican leadership offered Primo de Rivera in a prisoner swap that Franco rejected. In any event, we do know that they loathed one another. Once Primo de Rivera was dead, though, Franco went about building a cult of personality around him, going so far as to have him buried in the crypt of the Valle de los Caídos, the creepy massive mausoleum-basilica outside of Madrid where Franco himself was buried (until he was exhumed in 2019, but that's getting into the 20 year rule and a whole other question about Spanish historical memory). As I mentioned, I'm not too well-versed in post-war Francoist Spain, but I hope that this does illustrate at least in part that Franco was very much about co-opting the Falangist movement for his own ends.
In my own personal assessment, I would not call Franco himself a "true ideological fascist" on account of his hyper-conservatism and ultra-catholicism. He wanted to go back to a Spain that was, not forge some new fascist vision of the future. That does not mean that he was a pleasant dude, obviously, and the case can be made that he had a fascist worldview (for lack of a better term) especially through the lens of Eco. After all, Franco was obsessed with the idea that there was a massive Judeo-Masonic-Bolshevik conspiracyseeking to destroy God and Spain (as you may have suspected, there was no such conspiracy, but uh try telling that to a true believer). EDIT: This may be my deep disdain for the Nationalist band in the Civil War seeping in here a bit, but Chapter 7 of Preston's The Spanish Civil War, also cited in the addendum, contains a good overview of the ideological content/non-content of the Nationalist camp, particularly as it relates to the legendary and heavily mythologized exchange between Miguel de Unamuno and Franco's chief propagandist, General José Millán-Astray. Preston does get some of the details of that exact encounter wrong, but the gist of it is that what Eco would ID as ideologically fascist in the Nationalist camp's rhetoric is the traditionalism, the cult of violence (which is also attributable to the fact that they're in the middle of a civil war), and the anti-intellectualism and hate of dissent that goes hand in hand with violent traditionalism. However, all that said, the Nationalist band did not propose to create something new, it was instead deeply aligned with the Catholic Church (one of the traditional bastions of power in Spain, which was given control of the educational system after the war), and painted itself as sort of a interlude before the monarchy would be reinstalled. They heartily embraced rhetoric about this being a new Reconquista, with the Nationalists engaging on a crusade against godless Reds like their mighty Spanish ancestors of old had carried out against the Moors (never mind that a unitary Spanish state wasn't a thing until after the Reconquista, and how ironic this rhetoric was given their heavy use of Moroccan soldiers from the Army of Africa as shock troops). So essentially, a reactionary traditionalist dictatorship taking on the trappings of the new ideology of the day, fascism.
I hope that this gave you at least some semblance of an answer, I realize that this answer is a bit scattered and quite messy, mostly serving as an elaboration on existing answers on this sub on this same question. I would be happy for someone with more expertise on post-war Spain to step in to give further depth on this and especially on his later years, but in summary: Franco definitely co-opted existing movements of all stripes in his push for power, and while there is substantial debate over whether or not he and his regime was fascist, it may be safe to say for your purposes that he was not an unequivocal "hardcore ideological fascist."
EDIT TO ADD:
So I had thought of editing to add this point on the Falange's organization earlier, but now that this answer has been mentioned in the Sunday roundup, I felt obliged to do so. The Falange was not the most organized group within the nationalist camp, nor the most welcome or ideologically uniform (for lack of a better word). As Preston notes in his book on the Spanish Civil War (on pg. 224), droves of former Republicans and leftists joined the Falange to basically keep themselves from getting executed during the White Terror, to the point where the party's blue boiler suits became known as the salvavidas (life jacket). Franco's choice to merge everyone into the Falange (much to the chagrin of some hardcore Carlists [a rather interesting group of ultra-Catholic hyper-reactionaries who supported a separate line of pretenders to the Spanish throne from mainstream monarchists, one of whom would later become a Titoist but that's neither here nor there] and hardcore Falangists) was a way to keep a lid on this rapidly growing group that he and the other army officers considered at least somewhat suspect. I'd consider the military faction to be the most "organized" group of the Nationalists, but of course they lacked their own political party, and it's way easier to crib someone else's work than to put in the effort to make your own. Franco himself knew that lesson very well, since he had managed to climb to the top of the Nationalist military structure through deft maneuvering (and some claim by arranging for the death of Gen. Mola, his only remaining possible rival for leadership of the Nationalist cause, in a plane crash, though claims of Franco's involvement are sort of conspiracy theories, see Preston pp. 212-16 for more discussion of his political maneuverings and a bit on Mola's plane crash).