I have heard some historians say that the orthodox interpretation of Franco's status as a fascist is misleading. While he allied himself with fascist forces, they argue that while he was a rightist authoritarian his commitment to fascism was not strong, and that he essentially only adopted the branding of fascism as a way to present himself as an opponent of communism in Spain. I would like to hear some thoughts on this and get a sense of the dynamics of the debate.
When viewed from the outside, Franco seems like a fascist. Some historians (especially Marxist ones) still see fascism as the extreme conclusion of right-wing beliefs - if so yes, he was fascist.
But the mainstream definitions of fascism today stem from the 90s when historians of the subject began - for the first time - to read fascist literature as an important source for understanding the ideology behind fascist movements.
Roger Griffin is an excellent source (you can google him) but a good starting point would be to listen to this 7-minute discussion: http://www.pulse-project.org/node/569
Basically: no, Franco wasn't fascist. As you said, he aligned himself with fascists at times to achieve his aims, but he and his party did not want revolutionary change in Spain. Quite the opposite: they fought to maintain the (right-wing, religiously conservative) status quo through authoritarian rule.
Edit: source: I'm studying 20th century fascism. Happy to answer more questions.
Edit 2: See /u/GobtheCyberPunk post below: "So in summary fascism distinguishes itself from conservative authoritarianism in that it co-opts leftist critiques of capitalism in the service of nationalism, and often in its desire for military expansion in service of restoring national greatness (or perhaps 'Making it Great Again')."
There's been a few threads on this similar topic that might be of interest to you as well as the answers you've already received:
"Was Franco's Spain considered Fascist by most historians?" - 24/03/14
"How was Spain able to remain independently fascist until the 1970s?" - 21/05/14
"Spain During the Cold War" - 17/09/13
Among other threads that can be found here, Spain during WWII and Spanish Civil War sections of our FAQ
Followup/related: This may be better as its own question and be outside the expertise of discussants here, but in discussing Franco I can't avoid thinking about António de Oliveira Salazar next door in Portugal. Salazar ran an ideological ultra-nationalist project (the Estado Novo) from 1933* until his death in 1970, and the state carried on until the Carnation Revolution of 1974. Was Salazar's Estado Novo regime fascist by prevailing definitions? Early on he actually moved against parties and individuals who claimed to be fascist, and cozied up to religio-socialist ideas, but were they effect fascists themselves, particularly after absorbing many National Syndicalists (who were considered actual fascists) and dissolving their organization in 1934? I've never really known whether we can link him to fascism.
*Yes, the coup was in 1926, but Salazar (at that point Finance Minister) only became Prime Minister himself in 1933.