I think you're overestimating the logistic capabilities of Medieval polities and consequentially dealing with a flawed premise. Save for the Spanish Reconquista, the Norman Conquest of England, and the Crusades, I'd be more than willing to argue that there is no real example of a pre-modern total replacement of a governing system by violent conquest (and I'm not even convinced I should be counting the Crusades). More commonly, territorial conquest only really occurred in bordering territories where social and political systems were already predisposed towards facilitating an easy transition into a new governing order. Even in those situations where territories were not bordering, as say, in the Italian maritime republics or the Aragonese thalassocracy, absorption by a larger polity was only attempted or even really conceivable because the political climate was favorable (plus, a sea-route is nearly as good a guarantor of cultural and political overlap as a land border).

Your example with England and France, for example, only really has any applicability after the accession of the Angevin dynasty in England; a dynasty which came to rule a large territory sometimes retrospectively called an empire. But this wasn't due to any sort of systemic occupation: for centuries after the Norman Conquest, the english monarchy continued to have extremely strong ties to France and French politics. The english monarchy and court remained predominantly french-speaking, and more often than not, resided on their possessions in present-day France instead of England. You can imagine, then, how easy it must have been for the english monarchs to dialogue, interact, and even marry into prominent french families, whose dowries of land and promises of fealty allowed the Angevins to assemble and govern a formidable state and effectively divide France in half. In spite of the Angevin polity's near-total dismemberment by the french monarchy in the first decade early thirteenth century, the English monarchy's ties to France were sufficiently strong as to unleash the Hundred Years War a century later; and even then, the war was entirely fought in France. Sure, the English had the channel protecting their island home, but it's also worth noting that the catalysts for that war were very specific to mainland France.

Of course, on the topic of England, going back to the eleventh century there is a vary famous example of a wholly foreign ruler occupying an entire Kingdom: the conquest of England by William of Normandy. William's subjugation of England is an impressive feat of systematic occupation, given the resources and logistics of the time. However, William was aided by the fact that not only did he manage to do in the King of England at the time, Harold Godwinson, but he did him in when the ruling Godwinson dynasty held three of the six earldoms in England. In short, England was, almost by happenstance, particularly centralized at the time of conquest, and by cutting off the head of the snake at Hastings, William's job was made much easier. Did the English villagers say, "I guess I'm French now?" as you ask in your question? Not really, in fact the rather systemic and orderly state apparatus instituted by William allowed the English kings to turn their attention to their wealthier and more densely populated French possessions while leaving the English to, well, be English. Sure, the impact of a French-speaking ruling class created some interesting linguistic quirks (the anglo-saxon farmers raised cows —a germanic word— while when the animal was slaughtered the french nobility ate the very french-sounding beef) but by and large it is the newly arrived French who learned English, and not the English who learned French.

So what does it take to successfully seize a foreign terretory? It's fairly easy to explain conquests of proximate territories; neighboring Stem-Duchies or their post-Ottonian successors in the Holy Roman Empire all fundamentally spoke a mutually intelligible form of German (although I suppose you can make an interesting case for the the systemic eastward expansion of the German Reich into Slavic territories; but even there we're dealing with a very specific case of cultural domination over a neighboring society that is less technologically and politically elaborate than the dominating power). Most of the time, you get situations where the local elite are disgruntled and side with a new, rising political actor; as the Sicilian Barons did during the Revolt of the Vespers, defying their King in Naples and instead adhering to the Kingdom of Aragon. And Aragon certainly wasn't chosen at random; it was a powerful western mediterranean state to which they had strong economic and social ties. But even then, large-scale land acquisition was fairly uncommon. Rather, it's much more common to see piecemeal integration, sometimes through coercion or the mere threat of force, but equally as often because of the natural alignment of interests by the ruling elite. For example, in the tenth century, when the Republic of Venice was only a city-state, repeated expeditions clearing the Istrian and Dalmatian waters of pirates in addition to increasingly favorable commercial treaties with the Byzantines giving Venetian merchants astoundingly free access to eastern markets led the city of Pola, an important administrative center of the German Empire's nominal County of Istria, to be persuaded to swear fidelitas to Venice. In exchange for naval protection, Pola (and the nearby town of Capodistria) undertook to supply the Venetian fleet with an armed galley in time of war. And Pola's adherence to the Republic soon revealed to do more than provide Venetian shipbuilders with a new source of lumber from the heavily wooded Istrian interior. Pola is situated close to marble quarries; and it was with stones from these quarries that the city of Venice would pave its streets and carve its increasingly numerous monuments. By 1150, the whole of the Istrian coast would adhere to the Republic, having become a seamlessly integrated component of Venice's expanding economy.

On that topic, Venice's thalassocracy would be accelerated by the Fourth Crusade in the 13th century; however even this seemingly wanton act of aggression was mediated by a methodical expansion policy. In 1202, the wily Venetian Doge Enrico Dandolo had already redirected the fourth Crusade's to the dalmatian city of Zara, expelling the Hungarian administrators and tying the city, an important stopping-point on the Adriatic with an Italian-speaking ruling class, definitively to the Republic. By 1268, the Crusaders had seized Constantinople and the Venetians negotiated the right to their own quarter in the city, obtaining a series of rights for the sizable venetian expatriate population there. Along the way and for some time afterwards, Venice managed to secure the submission of nearly every major stopping-point along the Dalmatian coast and several islands in the Aegean Sea: in 1220 Cherso, in 1236 Arbe, in 1237 Ragusa, in 1254 Curzola, in 1278 Lesina. Already in 1212, Venice had seized its prize possession: the island of Crete, which they called Candia. All these maritime locations already had strong economic and social ties to the Republic, and submission to Venice only made these ties even stronger. I actually wrote about Venetian territorial expansion in this previous answer which you might be interested in.

As you approach the Early Modern Era, you start seeing more wanton power projection by european states, notably through colonialism. In Italy a similar phenomenon manifested itself whereby the European hegemon had a tendency to seize the two of the most important Italian states: the Duchy of Milan and the Kingdom of Naples. Why Milan and Naples and not, say, Venice and Rome? Or even Florence and Genoa? Well, it so happened that the Milanese and Neopolitans had, among other factors, a political class with strong ties to the european powers of the time. When Louis XII pressed his claim to Milan at the end of the 15th century (Louis' grandmother was Milanese, and besides, he held a grudge against Ludovico Sforza, the reigning duke) he founded a Senate of leading Lombard families to help him govern his possessions in Northern Italy. The task wasn't difficult, as prior to Ludovico the Milanese dukes had a history of francophilia; dialoguing with leading citizens to guarantee stable rule was certainly not outside of the ream of possibility. And importance of this dialogue must have been evident to Louis, seeing as his predecessor, Charles VII, had led the first French expedition in Italy with the goal of claiming the throne of Naples only to see his military victories undone by his utter lack of a support mechanism which did not allow him to supply himself. This certainly contributed to Louis' decision to strike a pact with Ferdinand of Aragon to partition the Kingdom of Naples, offering the Aragonese the whole of the Kingdom except for the city of Naples. The utility was twofold; the French King needed to neutralize Naples, Milan's principal ally (albeit a disgruntled ally, but that's beside the point) and had learned from his predecessor's experience that occupying southern Italy was a feat he was simply not capable of carrying out. Because Naples was pretty much propped up by Aragon to begin with, it made sense to come to terms. I wrote more on the early phases of the Italian wars and Franco-Spanish rule in Italy here, although there's certainly more room for discussion!