OK that makes sense Henri.
But I think Maria Teresa the queen of Louis XIV was primarily an Infanta of Spain being the daughter of Felipe IV (that family interests me because of the beautiful painting Las Meninas that Velasquez painted of Maria Teresa's younger sister) although of course I see she could have claimed the title of Archduchess of Austria.
[edit-now I see that the French tended to call her Marie Terese d'Autriche like you said but I wonder why it wasn't Maria-Terese d'Espagne]
Most of the Spanish Princesses Pre-1713 were almost always referred to be "Of Austria" because they belonged to the House of Habsburg, which was also referred to as the House of Austria. Also the rules governing the House of Habsburg gave any children descended from a member of the House of Habsburg, the title Archduke/Archduchess of Austria, also if you notice in Juan Carlos's titles contain, Count of Habsburg, Tyrol, both of which which come from the same rule. Which explains why they appear in the Spanish Style, by virtue of this descent though technically I think its only to be descendants in the Male Line.
I find it odd that Juan Carlos would be in line for the Legitimist Claim to France since the Succession Laws governing the French House of Bourbon is Agnatic Succession and Juan Carlos is descended from Queen Isabella II.