The thought was this: Sorcerers get their power from their bloodline. Who else gets power from their bloodline? Monarchs. It's a different kind of power (authority instead of arcane) but let's pretend they're analogous for a moment.
Thus, Sorcerers represent the ruling class, the aristocracy. Wizards have similar powers but they get them through work, learning, intelligence. In the pseudo-medieval/early renaissance social environment of D&D they're the new and rising class of citizenry, merchants, officials etc who got into power through their skill and wit, instead of inheritance. This kinda reverses the traditional Wizard-Sorcerer dichotomy (Sorcerers usually being represented as savage and unrefined) and I like that.
Bards, I suppose are the (also new) class of scholars and artists. DaVinci, Dante, troubadours, Khayyam, Machiavelli, Maimonides, Chaucer...They often mingle with, work with etc. the nobility, but hold little direct power themselves. They are often advisers and such. In line with classical reasoning, their abilities are mostly derived from the gift of genius.
Rogues are simple and obvious enough. Fighters can encompass a wide range of possible social roles but as PCs they are probably either mercenaries or named (not born noble) knights, working either for the oligarchs or the aristocrats. Knights that decide to serve a religion (as many crusaders did for example) become Paladins.
Speaking of religion, it's obviously the second pillar of authority in a medieval world. Opposed to the "profane" Sorcerer-aristocrats are the Clerics (the highest of them possibly carrying the titles like Bishop or Pope). (In this way we can also see that the fighter can swear allegiance to one of the three sides to fulfill one of the three archetypes, or distribute them between Rogue, Fighter & Paladin.)
We're left with the Ranger, Druid, Barbarian and Monk. If we follow the line of reasoning that magical power = social power, then the Druid must represent the third pillar of authority. We know that by the middle ages, pretty much all pagan thought was eradicated in Europe, but there were still plenty of heretics, and there are those that would have you believe the witches are an ancient tradition. So the Druid is a kind of outsider, heretic, a witch. His powers are in line with that. He is not unlike the Cleric, but (from a medieval point of view) he worships "Satan" or some such equivalent. The Ranger shares the druid's powers source, so they might be a sort of pagan or heretic warrior (like the assassins maybe). His bond to nature doesn't really fit that well (and is a clear Tolkien derivative) but like the Church has its Paladins, Nature|Satan has its Rangers.
It's tempting to fit barbarians into this heretic order but they're probably better left as some sort of foreigners (Huns, Mongols etc.). (The traditional painted Celt or skin-clad viking berserker stereotype has been gone for five or more centuries by this point, so they're a bit off.)
We're left with Monks, which, to me, were always the glaring outsiders in the faux-ren-faire default setting of D&D. With a more pulpy, non-European spin, a weirder, more S&S world, Monks can fit right in, but in this scheme here they feel quite off, particularly because their distinction from European monks and non-reliance on weapons (unheard of). You can try to repaint them as a sort of Friar Tuck figure, and side them with the Cleric branch, but there's the issue of not having any divine powers. I don't really have any good solutions for this. It's probably best to leave them as travelers from faraway lands but the "Shaolin monk at King Arthur's court" never rings quite right to me.
So there. It shakes the typical assumptions about classes up a bit and provides interesting implied dynamics of the society in this world, with many potential hooks and conflicts.