There's no denying that Cauchon is one of the main antagonists. He leads the trial that sentences Joan to death. Even though Cauchon is honestly trying to save Joan's soul, the whole putting her to death thing sure puts a damper on Joan's goals. In the end, Cauchon and Joan just have two totally different points of view. He thinks God speaks through the Church only. She thinks God can speak directly to her. There you go – protagonist vs. antagonist. You'll find a more detailed discussion of Cauchon in his "Character Analysis."
You can pretty much say the same things for the Inquisitor as you can for Cauchon. He helps run the trial that results in Joan's death. The old man does honestly believe that he is doing the right thing. In his view, the power of the Church is the only force keeping Europe from descending into satanic anarchy. Joan challenges some of their most basic beliefs by saying that she knows what God wants more than they do. Therefore, she has got to go.
The Inquisitor also is seriously concerned with the fact that Joan doesn't act like a typical woman. He thinks that society totally falls apart when people start challenging traditional roles. Check out his super-long monologue. He basically says that, when women don't get married and dress like men, it inevitably leads to polygamy, incest, and running around naked in the woods. Joan says she dresses like a man because it's just practical. She's a soldier so she needs to dress like one. Neither one will budge in their opinions, so it's off to the stake for Joan.
The Chaplain de Stogumber
The Chaplain is the closest the play gets to a villain, in comic book kind of way. He hates, hates, hates Joan and probably has a secret lair in a cave somewhere. (This is only a supposition on our part.) The Chaplain's main beef with Joan is that she continually defeats the English in battle. Being from England, he doesn't take too kindly to this and will do anything bring her down. When Joan's radical French Nationalism meets the Chaplain's radical English Nationalism, the sparks fly – literally. The Inquisitor and Cauchon are both disgusted by De Stogumber's blood thirstiness in the trial. In the end, though, he does a complete turn around. When he sees the horror of Joan's execution, he is disgusted with himself and spends the rest of his life repenting. Too late buddy, we still label you as the most antagonistic antagonist of all.
The Earl of Warwick is the guy that sets up the whole trial to begin with. He buys Joan from the Burgundians and delivers her to the Church. Unlike his buddy the Chaplain, he doesn't hate Joan. In fact, at times it seems like he admires and is bemused by her audacity. He is simply opposed to her for political reasons. Basically, Joan wants to give all the power to the King. If this idea catches on, feudal lords, like him, will have to do whatever their King says. This would suck (for the feudal lords at least). Guess what, Warwick, the joke is on you. Feudalism's days were certainly numbered by this point in Europe's history.