one of my AH/scenario books dealing with WW2 has this scenario, IIRC, Germany adopts a 'Mediterranean' strategy that requires getting Spain involved. From what I remember, Gibraltar falls, but the Spanish navy is sunk in an afternoon...
a successful Nationalist coup in 1936 (in which treasury is not looted by Soviets) might have Spain develop delusions of empire (redux) and join Axis.
IF Spain joined Axis one could assume u-boats would move (moving) to Canaries and Equatorial Guinea prior? not sure GB would want or need to occupy them immediately or how easy to do so?
OTL seizing the islands had priority should the Axis threaten them.
The US also studied occupying them as a nuetral, similar to the Icelandic occupation.
Moving the U-boats up to the Canaries and Equitorial Guinea prior suggests Franco has planned to join the war for some time, not as a spur of the moment decision to take advantage of the sudden and unexpected collapse of France. However, if it was then the Spanish would have made these places capable of holding out for longer in the event of the inevitable (but not necessarily immediate) British invasion. In any event as the Germans didn't have that many U-boats at this point they would have moved up to Cadiz and Ferrol as they're better placed for operations in the North Atlantic.
... (not sure how to read Portugal situation, occupying Azores relieve or infuriate them?) ...
They really didn't look at Spain like that. In fact Spain was Germany's link to Latin America through most of the war.One idea I always loved was that if Spain joins the war, Latin America gangs up on them and march all over their former oppressor.