How would any of this lead to Franco joining the axis ?
The fact that Franco wouldn't be in power if it wasn't for Hitler & Mussolini, and the fact that Nazis are poking right over the mountains; if Hitler wants to stop the Allies from using Portugal, he has to act fast, before a US/UK army lands. And the only way to do that is to go into Spain.
How about the prospect of a complete blockade of Spanish ports for imports? Don't forget that the US supplied Spain with the majority of it's oil.
Or the prospect of an allied army on one side, a german army on the other, and planes from both sides overflying it.
I doubt it still would be worth for Germany start a second front not to mention if Germany invades Spain, it would be to the benefit to allies .
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It's not a matter of being worth it; Germany would have to deal with the problem. Don't forget that Germany only got involved in the med and Greece, they were forced to go because of the overall strategic situation. Likewise, the assault on Norway & Denmark was forced in Germany in order to protect the iron imports from Sweden.