Charles is the King of France, husband of Isabel, and father to Catherine and Lewis. In the play, he seems like a decent enough king (although the historical Charles VI suffered from mental illness and was referred to as Charles la Fou or "Charles the Mad").
In real life, Charles played a very minor role in the Battle of Agincourt (his Constable led the French army against the English), but in Shakespeare's play, Charles appears to be a capable political leader. Unlike his son, the Dauphin, Charles never underestimates Henry's threat to his realm. Instead, he orders his troops to fortify Frances "towns of war" and says, "Think we King Harry strong, / And, princes, look you strongly arm to meet him [...] and he is bred out of that bloody strain / That haunted us in our familiar paths"(2.4.51-52; 54-55). Charles refers here to Henry's uncle, Edward the Black Prince, who terrorized France and caused them "too-much-memorable shame." In this sense, Shakespeare uses Charles as a mouthpiece to praise England. At the same time, we can see that Charles is shrewd and he knows what he's up against. Also, he's no coward and he refuses to back down.
Even after Henry's army defeats the French at the Battle of Agincourt, Charles proves to be a shrewd and diplomatic king. He agrees to all of Henry's terms and signs a peace treaty that puts a (temporary) end to fighting and bloodshed (5.2).