Historically, the only people on foot in the Medieval Era with two-handed or Great Swords were dismounted knights, and even they more often were using regular swords, maces, battleaxes, etc. The most common Medieval Era Great Weapon for infantry, in fact, was the two-handed long-shaft Axe.
Halbards had a brief popularity as auxiliary weapons in Pike units - the early Swiss pike 'blocks' for example, included halbards and the Landsknechts included 'double pay men' with halbards or two-handed swords - but the Landsknechts were Renaissance Units, not Medieval - Maximilian formed the first units in 1486 CE.
The English 'billmen', in fact were armed with a form of Halbard (added a Hook or 'billhook' to the blade and spear of the halbard), but that is the only large number of infantry I know of armed exclusively with the weapon, and, again, they were 16th century, or Renaissance Units.
The sad fact for everybody trying to add an Upgraded Swordsman to the Medieval Era is that there really was No Such Thing. The same 30 - 33" long sword that had first been invented by the Celts in 800 BCE, used by the Spanish Celtiberians, adopted by the Romans as the Spatha and used by Vikings and mounted troops all over Europe was still the most common 'sword' right up to the time when noblemen were bringing them to Gunfights and losing. The only Upgrade was the invention of pattern welding to give a better quality of low-grade steel in the blades after about 200 CE (a process invented by the Celts, or at least in Northern Europe). Some specialty units, like Saxon Huscarles (Hastings - armored men on foot with two-handed axes) had 'Great Weapons', but the vast majority of Medieval infantry were armed with spears, swords, or missile weapons unless they were dismounted knights.
Until around 1300, when the Swiss, Scots, and Flemish militia revived the pike, which became the most common infantry close-quarters weapon for the next 390 years - right through the end of the medieval period, the Renaissance, and into the beginning of the Industrial Era.
The facts should be another nail in the coffin of Civilization's artificial Unit Classes, but facts have never stood in the way of Game Design, so I wouldn't hold my breath . . .
