Regarding the subject of an independent Aragon under a son of Ferran II and Germaine de Foix: I posted a few drafts of a TL on the subject here a while back titled 'Jo, El Rei: The Trastàmara Inheritance'. Sadly, though, I never completed the project and have yet to resume my work. Perhaps someday I'll reboot the project (and no, I promise, this isn't self promotion

).
From what I have read on the subject and gathered from others with far more expertise on the subject of Iberian history than me (a lot of people, I might add), my own opinion is as follows...
If Ferran's son, the Infant Joan, is born healthy and survives infancy, he'll be a little under seven years old at the time of his accession (assuming that Ferran dies on schedule ITTL). Aragon does not have much of a precedent for an automatic regency by the queen mother and, given the provisions of Ferran's OTL will for the regency following his death, it is most likely that his bastard son,
Alonso d'Aragón, will be named Governor and Administrator of the Aragonese Realms. However, considering his advanced age, I wouldn't be surprised if Germaine assumes the regency after his death, since there really aren't many others in a place to do so. In fact, interestingly enough, the queens of Aragon long had a special right to summon the Corts if necessary, and so, she may be the
only person legally able manoeuvre herself into such a position in the event of a crisis.
As an aside, the nobility are going to be thrilled at the prospect of the personal union ending, as there were already complaints in Ferran's time of unwanted Castilian interference and influence in Aragonese affairs (such as state offices and military commands being given to Castilian nobles by the Catholic Kings).
It's also important to remember that the Revolt of the Germanies will be very likely to still happen more or less on schedule ITTL, considering the contemporary economic and social tensions in Valencia. However, as the Crown will be resident in Aragon and more focused on affairs there, it may not get as out of hand as it did in OTL. If Germaine is regent at this time, we can probably expect a swift response and a very harsh and bloody end: in OTL Charles appointed her his viceroy in Valencia, and she treated the rebels very severely,
personally signing most of the death warrants.
In terms of foreign policy, I disagree with some of what has been said in this thread. The Trastàmaras and the Habsburgs are going to remain strong allies, at least in the first few decades of Joan III's reign, for a number of reasons:
The careful marriage strategies of the Catholic Kings and their strategy of 'encirclement' have bound the houses close together and Charles V is, after all, Joan III's nephew. At this time in Early Modern Europe, family and dynastic ties like this still counted for something.
The Valois were the ancient enemies of the House of Aragon. The Castilians may have courted the French and been their allies at times (usually in the interest of opposing the Aragonese), but Aragon did not (save for some brief exceptions under Ferran II, which were largely for temporary convenience). The nobility (especially in Catalonia) wouldn't stand for any long term 'Franco-Aragonese' arrangement--and that means a lot in Aragon at this time, as the Second Estate had far more control over the Corts then in Castile.
Perhaps most importantly: it's completely contrary to their dynastic interests. The involvement of the Catholic Kings in the Italian Wars had more to do with Aragonese interests than anything else (Ferran largely directed foreign policy from an Aragonese viewpoint during the couple's marriage); and Aragon, from a geopolitical perspective, has one primary goal: maintain possession of Naples, Sicily and Sardinia at all costs*.
The Habsburgs will remain opposed to the French in this scenario, given the dynastic and geopolitical baggage of the Burgundian inheritance and the need to prevent French influence so close to home in Milan by keeping the Sforzas in power (something within the mutual interest of both Charles and Joan).
If Ferran still annexes Navarra in this scenario (also very likely, given his ambitions there, the past history of Trastàmara influence and Germaine's own convenient claims to its Crown), he will do so for Aragon and not Castile. The Albret family are French allies, and keeping Navarra means opposing the French and any attempts they make to reinstall them there.
Also, apart from Italy, there will be a lot of focus on the Western Mediterranean and preserving Aragonese domination there, especially in North Africa. The Barbary Pirates (and thus, by extension, the Ottomans) were a constant headache for Aragon. With Ottoman aggression likely in Hungary and Austria as in OTL, the Habsburgs and Trastàmaras share another mutual interest in opposing their expansion in this respect. In this scenario, François will have just as much reason, if not more, to pursue an Ottoman alliance as he did in OTL, which is
very contrary to both Habsburg and Trastàmara interests.
*Interestingly enough, in the marriage treaty between Ferran II and Germaine de Foix, Louis XII renounced all claims to Naples in favour of the couple's future male issue, but reserved the right to continue his claims in the future only in the event that the marriage proved childless.
EDIT: Apologies for the length of this post, but I figured that I could at least contribute some thoughts to the discussion.