The irony is that the Normans were far more likely to be using spears instead of swords, which are more like the lances that William was using to become a noble. Nobles would have carried swords, but they were status symbols and treated with religious reverence. They would only be used in battle if the spear was thrown or broken.
Novels, mythology, folk tales, swords have always been romanticized. Nobles that carried them would have holy relics (bits of dead saints) encased in the pommels. A well-made sword was a strong weapon, and its owner probably trained in its use.
Like imagine you're a pikeman, probably a farmer by trade, hungry and cold, wearing padded leather and salvaged cowhorn scalemail, probably injured or sick, and you are in the fracas of a battle. You see a mounted knight wearing proper chainmail armor, healthy and strong, rested because he didn't have to walk to the battle or dig a latrine to shit into, and he's got this shiny, sharp, holy weapon engraved with magic words you can't read. He's already broken his spear off in your friend, and now he's waving his blessed +2 Steel Longsword in your direction.