Even with England-wins-HYW scenarios the general consensus seems to be that even by that stage, so long after 1066, the English nobility was still so 'French' (well, strictly speaking Norman) that the matter of two different cultures wouldn't be an issue; the nobility would be largely of the same culture. A French nobility would rule French peasants in the Plantagenet kingdom's Continental possessions and a French nobility would rule English peasants in England. In this scenario, with the union occurring even earlier and without the Hundred Years' War to give the French such a strong hatred of the English, that would therefore seem to be even less of an issue. Unless we're positing major peasant rebellions then it's the nobility who will choose whether or not to rebel, and I don't especially see why they would. For all that we might think of England and France being inevitable rivals, in this situation their proximity could be a strength for Anglo-French cooperation rather than a weakness; commercial links across the Channel could grow so strong that separation would be very difficult indeed.
The population of France at this point exceeded that of Great Britain by such a vast amount that I wouldn't think that the fleet would be so 'British'; indeed, even if the proportion of 'Britons' who joined the fleet was twice as high as that of 'Frenchmen', the French would still be dominant in numbers there.
The biggest butterfly, barring the New World (and I agree that Britain-France will hold even greater lands in the New World than Great Britain and France put together did IOTL, since it won't undergo costly wars between Great Britain and France), will be European power politics. Britain-France will be incredibly powerful, more so (I think) than any other country in Europe unless we posit an HRE with strong central authority. That means that the entire balance of power is shot to pieces. I'd suspect that Britain-France will often face large groups of nations as its enemies.
As for the point about a split between sons, well, I don't deny that it's possible, but that would be sort of going against the spirit of the OP, wouldn't it?