To be fair, France's population just kinda kept going back and forth between various numbers between 16 and 20 million from 1200 to 1700. It didn't actually grow.
Then again, you're forgetting the Great Plague, that ravaged european demographies (killing off between 1/3 and 1/2 of the population).
Depending of the guestimates, it means that from a population with 20 millions in mid-XIVth century, it felt up to 12 by the XVth, only to turn back to 20 millions in 1500.
Reaching your original population after a loss representing 2/5 of it, in less than two centuries (in spite of being in a really unsecure context, socially speaking) is what I call demographical dynamism.
The apparent stabilization of the next two centuries can be partially explained by the context, rather than "ho no, medieval people stop to breed and France lost all its population forever" while the regular loops are more easily explained by their imediate context. By the XVIth century, Wars of Religion and climatic impairement of the second half of the century certainly prelieved their tool, or with Louis XIV's wars (or again climatic issues of the early XVIIIth century).
The Hundred Years War may have accelerated the political split between the English and French nobility but the English were already definitely English.
Basically, you may confuse linguistical and cultural distinction (that was, I wholly agree quite clear at this point) and clear
political dinstinction : nobody really saw harm in the King of England ruling over parts of France (and generally not his subjects), unless in term of dynastical interest for Capetians.
Not that you didn't have a political distinction (that is more a product of the cultural and legal shifts of the XIIIth century than the result of Capetian/Plantagenêt wars; but it didn't realised itself until the HYW at the point it was clear not only for the nobility and elites, but for popular classes as well, on all the kingdom.
Of course, it wasn't the only part that made a french national identity appear, far from it : hints of such thing appears since the late Carolingian period in struggle with Ottonians and when people ceased to say
Carlenses to name the inhabitants of Western Francia.
But, the HYW represented a clear qualitative jump, with a popular identity no longer based on dynastical ties but as well on culture and political identity and present within all the kingdom.