French Italian ambitions was what Habsburg Austria-Burgundy and Trastamara Castille-Aragon brought together. Not to mention that the Habsburgs already inherited a rivalry with France as the heirs of Valois-Burgundy, a rivalry which can be traced back to the rivalry between the Orleans and Burgundy branches of the house of Valois.
Anyway for the Habsburgs their original main concern was to prevent France from getting the duchy of Milan, whereas the Trastamaras initial concern was the kingdom of Naples. This basically made them natural allies, since they had a common foe and not many conflicting interests.
The reason that the Habsburgs were concerned about Milan is quite simple, it's a part of the Empire, but more importantly it's dangerously close to the Habsburg Austrian Hereditary Lands.
@ Alpha Trion: the Habsburgs had similar considerations as their Spanish and French counterparts to stay Catholic, they too wouldn't gain much from converting.
You also made a good point about the balance of power, IOTL the realms of Charles V (I assume they also include those from his brother Ferdinand I) and France were roughly equal, England was in the position, that it could tip the scale in some side's favour.
However IOTL the Habsburg Netherlands were one their most valuable European possessions, the tax income was thrice as high as the tax income of Naples and Sicily, only eventually surpassed by Castille, however the Habsburg Netherlands were able to provided loans*, which were twice as high as what Castille could afford.
Still even without Habsburg Spain, France and Spain are bound to become rivals anyway, however holding together alliances will be harder ITTL.