Cauchon is an honest kind of guy. He is loyal to the principles of the Church. He refuses again and again to compromise his fundamental beliefs for the sake of politics. He lashes out at Warwick saying, "You great lords are too prone to treat The Church as a mere political convenience" (4.77). This is one of his favorite things to say to Warwick. He reiterates it like a billion times. It seems as if he really means it. Cauchon sticks to his guns throughout Joan's trial. Warwick keeps pressuring him to go ahead and toss Joan in the fire. Even though 800 English soldiers are surrounding him, Cauchon declares, "I am determined that the woman shall have a fair hearing" (6.27). He does exactly that, at least according to the principles of the Church.
The Bishop is a bit like one of those robots on Terminator. At all costs he must defend the Church. He is programmed. At the trial he declares, "The mighty structure of Catholic Christendom […] may be […] brought to barbarous ruin and desolation, by this arch heresy […] Protestantism." By Protestant he means somebody that thinks they know God's will better than the Church. Hmm, sounds a lot like Joan (6.71). The Church declares that her voices are demonic. She says they're from God. Cauchon has no choice. He must terminate. When he comes back in the epilogue he says, "I could do no other than I did" (E.64).
We should point out that our Terminator reference is a bit unfair; Cauchon isn't totally inhuman. He expresses reluctance at going to see Joan burn and shows real concern for her soul. He's also obviously disgusted by the Chaplain's bloodlust. After his death, he is not remembered for his dedication or compassion. The hearing that restores Joan's good name destroys his reputation. They even go so far as to dig up his corpse and throw it in a sewer. In the epilogue his ghost laments, "They will be the worse for remembering me: they will see in me evil triumphing over good, falsehood over truth, cruelty over mercy, hell over heaven" (E.64).
This is pretty much the case with the historical Cauchon. In most histories and indeed in most other fictional versions of Joan's story, he is depicted as corrupt and in the pocket of English. Shaw claims in his preface to Saint Joan, that, upon examining the transcripts of Joan's trial, he found no irregularities. Cauchon was just doing what he had to do. Shaw does admit, however, that he may have perhaps "flattered" Cauchon a bit, in the interest of having there be "no villains in the piece." He goes on to say, "It is what men do at their best, with good intentions […] that really concern us." Shaw's depiction of Cauchon is exactly that: a man only trying to do what he believes is right.