Franco recieved military support from both Hitler (Legion Kondor) and Mussolini (Corpo Truppe Volontarie) during the Spanish Civil War. And, when this war finished, Franco, Mussolini and Hitler were very close friends.
So, when the Invasion of Poland happened, and the WWII started, why Spain never supported them in an official way?
I know that several spanish participated as volunteers in the German Army (the Blue Squadron), but there has never been a full and official support
TL;DR - Portugal and Britain.
Portugal was reasonably Allies-leaning just as Spain was reasonably Axis-leaning. Portugal, although under an authoritarian government, had stronger political and economic ties with the Allies. For this reason, both sides believed whole-heartedly that if Spain joined WWII as part of the Axis, Portugal would join as part of the Allies. The reverse is also true. The main reason for this was the Anglo-Portuguese Alliance, a pact between Britain and Portugal which has been in place since the 1300s. It was widely believed that the British would invoke this alliance to call Portugal into WWII should the need arise.
This would open up a new front many hundreds of kilometers long and probably divert both British and German troops to deal with it. The Portuguese had richer African colonies and other regions such as Macau and East Timor to utilize. Also important was that a Portuguese entrance would allow the Allies even more access to naval/aerial bases near Africa and the Meditteranean Sea. Spain, on the other hand, had a larger army, navy, and population, and could open up its own military bases (especially important as Italy crumbled in '43) to the Axis.
Franco himself didn't want to deal with an entrance into the war because the British navy and air force were performing fantastically against their German counterparts, which endangered Spain as it might be surrounded on all sides by British boats and bombs should war break out. Transit through the Pyrenees between Spain and France was slow, which meant that a sudden conflict could leave large-scale German reinforcement quite a while away.
The simplest way of describing why Spain didn't join the Second World War is that neither side wanted to deal with a third front, but there are other reasons. One was that Hitler thought Francisco Franco was an idiot, and infamously said that he would rather have teeth pulled than have to converse with him. Interestingly enough, the most important meeting of Franco and Hitler at Hendaye, France ended with Hitler threatening to annex Spanish territory into Vichy France. Talks fell apart soon afterwards.
Edit: I somehow misspelled Vichy France as Vichy Spain. Nevermind that.
To stop Spain joining war, US sold the oil to Spain. (And Spanish sold them to German. That's why US soldier saw US oil in German.) Though US knew that, they kept selling to hold Spain
It's also worth noting that, in addition to the very thorough geopolitical answer above Franco wasn't really a fascist in the strictest definition due to his use of religion as a basis for his movement. Fascism places the nation above all else, including the church. Rather he received support for his fight against the republic from Fascist and Nazi powers due to their common enemy and a mutually beneficial desire to test/ use modern arms in the spanish conflict.
Franco was a rather pompous leader and would not have taken kindly to being the least valued member of the axis, nor was there anything he could gain by doing so. Franco didn't have much to contribute in terms of military hardware as the Spanish Civil war had been something of a change in warfare and much of the modern technology he relied up on came from the Axis powers. Spain was better served by remaining distinct from the conflict and dodging the international limelight as it purged after its own Civil War.