Desiree Clary is right when she says that Franco's troops were being ferried across from Morocco. They were also protected from the loyal Spanish navy's intervention by the German pocket battleships (like WWi battlecruisers) Deutschland and Admiral Scheer, the latter escorted Franco's troops to mainland Spain. At the same time the first major airlift of troops in history started.
The airlift started with a few French Breguets, Nieuports and Italian Savoias. The major transport from North Africa to Spain was conducted by Junkers52s sent by Hitler. The Loyalists were deterred from attacking the transport vessels of the Army of Africa by the presence of the Deutschland and Admiral Scheer battleships openly supporting the rebellion.
In this way the insurgents were able to transport heavy equipment to Cadiz and then to Sevilla to consolidate the rebellion in the south of the peninsula.
The airlifts were started with these ancient old planes. French Breguets, Italian Savoias and French Breguets, but mostly by Junkers 52 supplied by Hitler.
Ref: The Battle for Spain, Antony Beevor, pages 71- 73 ISBN0.14.30.3765X, published 1982.
When looking for the reason why things go wrong, never rule out stupidity, Murphy's Law Nº 8
Those who do not remember history are doomed to repeat it. George Santayana
"Ach du schwein" a German parrot captured at Bukoba GEA the only prisoner taken