D'Artagnan is originally from Gascony. Why is this information important?

To a large extent, Alexandre Dumas restored the somewhat damaged reputation of Gascons in The Three Musketeers. For centuries they had been mocked by France's educated elite for their rough manners, their ignorant country ways, and their mangling of the French language. Yet Dumas chooses to emphasize another characteristic of Gascons: their extraordinary bravery. And D'Artagnan is representative of this.
During the seventeenth century, when the story is set, Gascons were massively overrepresented in the French Army. They had a reputation for being brave, fearless fighters, utterly loyal to the king, and completely reliable in battle. Two centuries later, their reputation for physical courage on the field inspired none other than Napoleon to exclaim,

Give me an army of real Gascons, and I’ll cross a hundred leagues of hell!

In that sense, D'Artagnan is almost the archetypal Gascon. He has all the good sides and bad sides—including pride and impetuosity—traditionally associated with folk from that neck of the woods. His earthiness and fundamental decency, his innate sense of what's right and wrong, stand in stark contrast to the widespread cynicism, world-weariness, ostentation, and greed of the Parisian court elite. Dumas appears to be suggesting that France needs to draw upon the old Gascon values to become great again, and it is in the brave, honest, plain-speaking figure of D'Artagnan that those values are most evidently displayed.