The trial for heresy was politically motivated. The tribunal was composed entirely of pro-English and Burgundian clerics, and overseen by English commanders including the Duke of Bedford and the Earl of Warwick. In the words of the British medievalist Beverly Boyd, the trial was meant by the English Crown to be "a ploy to get rid of a bizarre prisoner of war with maximum embarrassment to their enemies". Legal proceedings commenced on 9 January 1431 at Rouen, the seat of the English occupation government. The procedure was suspect on a number of points, which would later provoke criticism of the tribunal by the chief inquisitor who investigated the trial after the war.From this excerpt you can clearly see that her trial was hardly a model of justice and impartiality. But the very idea of a trial, and an appeal to fairness and an authority beyond the people with the most swords, is what is remarkable. Yes, the English bent rules, but there were rules to follow and they had to give at least a minimal appearance of following them. They didn't just immediately and gleefully execute her with no explanation beyond "she frustrated our goals and we don't like her."
Under ecclesiastical law, Bishop Cauchon lacked jurisdiction over the case. Cauchon owed his appointment to his partisan support of the English Crown, which financed the trial. The low standard of evidence used in the trial also violated inquisitorial rules. Clerical notary Nicolas Bailly, who was commissioned to collect testimony against Joan, could find no adverse evidence. Without such evidence the court lacked grounds to initiate a trial. Opening a trial anyway, the court also violated ecclesiastical law by denying Joan the right to a legal adviser. In addition, stacking the tribunal entirely with pro-English clergy violated the medieval Church's requirement that heresy trials be judged by an impartial or balanced group of clerics.
Compare: confronted with the victorious army of Kublai Khan, the last Song emperor jumped to his death along with other high-ranking officials, rightly fearing their fates should they fall into the Mongols' hands. Was there a court they could appeal to for release or at least better treatment? An argument they could make to Kublai from universal moral authority, about what was the right and fair principle to obey? How could these concepts even make sense? For China and the Mongols, there could be no appeal, indeed no idea of an appeal beyond either's physical authority as it stemmed from each mans' desires - that is to say, force.
The benefit of an organization whose authority was mostly moral is something that those of us who are secular-minded may ignore, as it stemmed from supernatural claims. We are often tempted to write off medieval Europe as a thousand-year failure mode, an Iron Age Orwellianism, or a Mad Max dystopia from the standpoint of ancient Roman citizens. While it was all those things, the seeds of Europe's positive divergence were being sown, and having a superimposed moral authority, separate and acknowledged by all as above Earthly concerns, was a unique arrangement and seems likely to have been part of it. There are many ways to think about this - two might be that warring parties both respecting the Church's authority created an in-theory neutral arbiter; another is just that more players makes a richer political ecosystem that is less zero-sum. This ultimately made possible rule of law and not of men, the possibility of service to principle rather than person. The destructiveness of rational warfare in eg East Asia was possibly part of why Europe was able to pull ahead.
It may have been quite fortunate that the church was based in one city that fell to barbarians (Rome) and another that saw its territory shrink until it was overwhelmed by infidels. The Western Church then was a kind of virtual state that could coexist with the others fighting for survival in Western Europe. It was a fortunate accident of timing, with Europe's isolating geography (mountains near the coast and indented coastlines) favoring continued separation. In an alternate history where Belisarius succeeded in reuniting the Roman Empire, European religious history might look much more similar to that of the Middle East, where religious and political authority were inseparable (or Chinese history where it was clearly peripheral) and there was no chance for mediation to calm wars and allow the concept of rule of law to emerge.
This 2018 paper by Hill, recently covered on MR argues in more detail about why the concept of the rule of law emerged when it did, though I disagree that it's the ideology itself that was more disposed to resulting in such a concept, rather than the geographical, political and military context of each. That is to say, if we re-ran history with the holy books switched, eg Mohammed in a cave writing the Bible, and the Qu'ran getting vetted and adopted at the Council of Nicea, I think the result would have been largely the same.
In the twentieth century, the U.N. has clearly appealed to a sense of universal rights much more than previous international forums did - the League of Nations and the Concert of Europe before it were both practical negotiation venues, but the U.N. makes claims to mediating universal morality. I can't help but wonder to what extent that has been intentional, and can't help but worry even as an atheist that it's easy to for states and peoples to reject non-supernatural moral claims as being made up by human beings, only and always for pragmatic self-interest.