On the surface, it seems reasonable to expect it. Hitler and Mussolini had both supplied him with arms during the Spanish Civil War, and he ruled under a Fascist dictatorship. I understand that Hitler and Mussolini were allied after the break down of the Stresa Front & Anschluss, but why would they exclude Franco from the war?
Would Franco not be eager to return the thanks to the two leaders who's rule he mimicked and who got him to power initially?
I study International Relations and I came across an article called "Wedge Strategy, Balancing, and the Deviant Case of Spain, 1940–41" by TIMOTHY W. CRAWFORD
Crawford claims that Spain was kept out of WWII by Britain who provided significant economic aid to Spain in order to keep them from the obvious alliance with Hitler. Crawford describes that Spain was put in a dire situation as they faced major economic problems resulting from the destruction of their civil war. Britain took advantage of Spain's economic turmoil to keep them away from the fascist alliance by offering them economic aid, taking advantage of the Germans being slow to act (The Germans obviously had plans to bring Spain into their alliance but acted slowly and indecisively).
Why would Britain do this?
1)First and most obvious the addition of (however limited) resources to the fascist alliance would be detrimental to the Allies.
2)Britain wanted to keep their access to the Strait of Gibraltar which would have almost certainly been taken away from them (either by force or other means) should Spain join the opposing camp.
This is the explanation that I am familiar with, I'm sure it's not the only and it may not be the best but I hope it gives you a little insight.