An issue dear to my own heart here, since I'm a modern sport fencer more than the rest of it. You read fantasy literature sometimes, and the hero is holding a sword one handed, waving it about, and fighting solely with that sword. That is certainly what we do when we fence, because that is what the rules tell us to do. Is it what your hero should be doing, though? Should they be holding a single blade one handed, holding two blades, carrying a shield, using the sword two handed, or something else? For today, we'll deal with holding something in either hand. (Two handed weapons to follow).
A single one handed blade is common in fencing mostly because it became the prominent mode of the later European duel, where the emphasis was on making things very even to force an advantage in skill to prevail (I'll be talking about duels and battles later). It also shows up in some other sword schools when you have a relatively light blade to hand, but nothing else. That doesn't mean it represents the most effective approach to swordplay in all circumstances.
In a lot of cases, your hero should be doing something with their off hand. They might hold a short dagger, or a lighter sword (the Japanese katana/wakizashi combination, for example, or the sword and knife of western rapier stuff or escrima). They might have a cloak, to let them tangle the opposition blade. They might even use the spare hand to grab or trap the opponent's arm/blade after an initial parry. This is the lock and block stuff of Filipino systems, but also shows up in longsword work after the initial clash.
Or they could hold a shield. Shields are a special case. They are not passive. You don't just sit behind them. You actively look to deflect with them, or trap blades with them, or hit the opponent. They come in all sorts of shapes and sizes. Not all cultures used them. The Japanese seem to have eschewed them in favour of that second sword, for example, while the Spanish favoured rapier and dagger. Note that they can even show up in environments with fencing weapons. Early rapier masters who came over to England from the continent got lots of followers, but lost several fights with broadsword and buckler experts.
So don't have your hero doing nothing with that back arm. Unlike fencers, they don't get carded out of the competition if they happen to put it in the way, or grab a sword hand, or punch someone. With two hands, they can kill twice as many goblins, after all. (I'm expecting letters from conservationists shortly).