If what Dr. Nicolle is saying is true, then the weapon to the left isn't a godenac but more likely a early form of falchion. Below is another view of the falchion. This one has a counter curved pommel to possibly help control the weighty end. dr. Nicolle:

Falco, falcione: [Early Italian] form of staff weapon, perhaps like the French  faussar, or early form of falchion; Italy, 13th-14th centuries. [puricelli-Guerra: the glaive and the bill]

Fauchon: [old French] early form of single-edged falchion, generally a infantry weapon, France mid/late 13th century [oakeshott: the archeology of weapons]

f 14 v 98. Noticing the way this figure holds the weapon, we can surmise that the sharp edge of the blade is upwards with the scalloped part on the backside. This panel also allows us to see what could be a reinforce backside or thicker spine [against his shoulder].

In the back ground of this panel are an assortment of weapons: war club, sword, a short-pike or what may actually be a godenac, another of the early falchions and a Danish styled two handed ax.