I could be wrong here, and someone else probably has better knowledge at hand, but I think around this time most warriors are still using spear, axe and shield. In Roman times, the Spatha developed over time as a cavalry sword, long enough to be used from horseback. The Gladius remained the infantry sword until after the fall of Rome. Swords, particularly Viking, were symbols of prestige and wealth, and were not readily available/were too expensive for most to own. But just about everyone could own a spear or an axe (which also has other uses). The archaeology is still not very clear on this, but I think that swords are more of a Hollywoodism, and "look cool", which is why they're so ubiquitous in games. They also appear in ancient sites because there is enough metal remaining to be found, while spears don't. Axes, Maces, Polearms (Spears), and Hammers were all much more effective in combat, particularly when the opponent was armored.
*edit, and I do realize that Rome fell long before 1000AD. I'm just using the Spatha, since it was mentioned, as an example of a specific weapon that developed for a specific purpose. The spatha as a slashing (not thrusting weapon) had no utility in a block of infantry behind shields.
The other element of DnD that often doesn't make sense, is that a lot of weapons and tactics were used en masse, ie. in formations. DnD is usually concerned with "skirmish" style fighting. And in skirmish style fighting, a lot of the weapons would be impractical (pikes, lances, bows, etc.), but highly effective in blocks.