Likely the biggest reason was exhaustion. The casualties taken during the Spanish Civil War were a huge drain on the nation. Also, Franco was determined to continue to "cleanse" Spain of leftist influence--as well as any potential rivals for power. Having executed roughly 150,000 noncombatants during the war, another 100,000 were killed in the years immediately following it. Many more were imprisoned. Franco was offered a number of incentives to enter the war by Hitler, but he consistently asked for more--more than Hitler was willing to concede. Franco did allow a division of Spanish volunteers to fight on the Eastern front for a time--the Blue Division--but they were withdrawn after a while so as to not antagonize the (western) Allies.

I think we also need to credit Franco's survival instinct and savvy. With France on the ropes in 1940, Franco declined to enter the war. He did the same when it seemed Russia would collapse a year later. Why? Because he had little to gain by joining the war. If Hitler won, then securing Gibraltar would have been easy, as would potential conquests in Northern Africa. But if Germany lost, Spain would be exposed to fighting the US and UK, which would have been overwhelming. Later, Franco's staunch anti-communist stance made him useful to the US and UK in the developing cold war. Franco's ability to survive and maintain power is perhaps his greatest strength, and he demonstrated that ability in not joining WWII.

None of this is to say that Franco was the head of anything but a regime that was "barbarous." That's Jose Sanchez's word for it, and I think it is apt. That doesn't stop us from being able to recognize Franco's ability to play various factions against each other for his own benefit--demonstrated during the Spanish Civil War and afterwards.

The relationship between Franco (who was a conservative authoritarian dictator — saliently not a revolutionary fascist) and Hitler is complicated, but they certainly weren't friends.

Both Hitler and Mussolini viewed Franco with some wariness, verging on contempt; their involvement of Spain was driven by selfish motivations — mostly around using Spain as a testbed for military forces, technology and doctrine — and shared ideology inasmuch as none of the three wanted to see a communist/socialist Spain, and certainly not one that acted as a Soviet proxy.

Spain wasn't ready for war in 1939 — an incredibly bloody and divisive civil war had just ended, and the new nationalist regime was still in its nascency. Spain's army was far from world-class; it may have been able to defeat the republican forces, but that's a very different thing to taking on other national armies; its navy and air force were equally sub-par.

Spain's last international war, in 1898, had been an unmitigated disaster that dealt a hammer-blow to Spanish national pride and civil society. But Spain's neutrality during the First World War had reaped significant economic rewards — it dramatically accelerated industrialisation (of an economy that had lagged behind the rest of Europe for most of the preceding century), and enabled Spain to become a major exporter to both sides.

None of which is to say that Franco didn't consider intervention: there was a prolonged conversation between the Axis powers and the Spanish regime, over the nature and timing of a potential Spanish entry into the war. Eventually, a meeting in October 1940 between Hitler and Franco at Hendaye ended in deadlock; Franco decided that Spain would remain neutral — though the Axis intelligence services were allowed a free hand to use Spain as an operating bases, and an all-volunteer Spanish division (the División Azul) was formed and sent to fight in Russia.

Franco was a thoroughly pragmatic statesman, and any intervention would only have happened if he was confident he was backing the winning side. But even in 1940, at the height of the Axis' success, going to war with both Britain and France could have had dangerous consequences (that, in part, is why the División Azul was exclusively deployed on the Eastern Front — that was a stipulation of its formation.)