I´d say Spain did not have any real war aims.
-They were overburdened with the rest of their colonial empire already,
so entering the war to get a larger chunk of North African desert doesn´t make sense.
- The same applies for gains on the continent: The Spanish didn´t have any irridentistic movements, an invasion of Portugal doesn´t make sense, and annexing parts of France would bring in
a) a French minority
b) more Basques (exactly what the doctor prescribed,

)
So that is out of the question for someone with concerns about the purety of the Spanish, or let´s call it the Castilian Way of Life.
So without any genuine war aims and unsolved issues with the neighbours
a war is unlikely.
If he entered the war on the german side, a quick look on a map shows that he is very vulnerable by seaborne attacks, would require the assistance of the german army. So aside from this assault on spanish pride, I would imagine that Franco would fear of being no longer master in his own country.
Also, the country was depleted from the hardships of a 3 year civil war, and the equipment of the army became rapidly outdated.
Lastly, I´d suppose that the ruling elites in Spain were also a bit thankful for the important assistance by high-standing circles in Great Britain and the US.