Most likely scenario.Althought,it could happened in 1756,too.
No matter which date we take,we would have united catholic America under Stuart rule.
Or not - in OTL England supported rebels in spanish colonies,now they would support Spain to crush Stuarts.
A lot of it depends on the circumstances in Europe. With such an early POD, we can't assume things to be the same, but the basic cycle of European wars will no doubt be ongoing.
In the event, we're postulating a French-backed war for independence fought by the British North American colonies during (OTL) Queen Anne's War. This results is (I suspect, considering the autonomy of each colony) a confederal entity called something like "The United Kingdoms of America", swearing loyalty to the Stuarts. (Who style themselves "King of England, Scotland, Ireland and the American Realms" or something like that.)
Some time later, the Stuart line moves to North America after their risings in the British Isles definitively fail. This would initially be the Young Pretender going over to reign as his father's representative, while the Old Pretender would still perpetuate his claim to Britain. But after the OLd Pretender dies, I think the Young Pretender would just style himself "KIng of the American Realms" and be done with it. (This scenario would prevent his OTL marriage, and an ATL marriage could plausibly produce heirs -- he produced an illegitimate child in OTL, after all, so it's not like he was incapable. Thus, we may assume that that the Stuart line is secured. In giving up any -- active -- claim to Britain, he'd make things a lot easier for the Papacy, so his kingship over the American states would be recognised forthwith, by all Catholic powers.)
Some time later still. the French colonies in North America become increasingly unwilling to stay subservient to the King of France, for the same basic reasons that also motivated the British colonies in OTL. Since they're Catholic, and so is King Charles Stuart, I think they'd join with him. With would happen after the Old Pretender has croaked, so after 1766. At this point, King Charles would have no direct loyalty to France, and backing the French colonies would only see them join his realm.
I think Britain would sit on the side-lines, cackling about it all. The colonies would win their independence, thus reinforcing the precedent of successful American independence wars (already set when the British colonies split off), and setting the new precedent of Catholic break-away states joining the Stuart monarchy voluntarily and prospering by it.
Finally, we'd see the discontent on the Spanish colonies, which would translate to the obvious goal of "win independence from Europe, and join the Stuarts like the French colonies did, under the same terms". This resolves their internal conflict, because it allows them to break away from a mnarchy they feel mistreats them, but absolves them from the sin of going against the divine right of Kings. (They're just joining
another Catholic monarch -- something that has happened in Europe a thousand times!)
Would Britain support Spain in this case? I see no reason why France and Spain would cease being allied. This means Britain is still opposed to the Franco-Spanish, and a revolution against these powers would be...
good for Britain. So much as in OTL, I could see the British even tacitly supporting the independence movements.
Especially if the Stuarts have given up their claims to Britain, and are content to rule in America.
In any case, the ultimate result -- a very large, independent, culturally Anglo-Franco-Spanish union of Catholic realms in America, under the Stuarts, reaching at least to the Isthmus of Tehuantepec (and possibly beyond) -- is a fascinating one to consider.