Did Saint Joan receive a fair trial? Why, at the end, was Joan excommunicated and burnt?

Joan of Arc was not a typical prisoner of war. Following
her capture by the Burgundians, she was not allowed to be ransomed, as was often the
case. The French King Charles VII refused to step in on her behalf, so she was left at
the mercy of the British court after the English purchased her from the Burgundians.
Because the Duke of Bedford had claimed the French throne for his nephew, Henry VI, and
Joan had supported his rival, it was determined that she had attempted to weaken the
power and authority of the king. Thus, the charge of heresy was made against
her.

Although no true evidence could be found against Joan,
as required by law under charges of heresy, the trial began anyway. Church law was
violated when Joan was refused legal counsel. Joan's own testimony was wholly
believable, but the transcript of the trial was later altered to her disfavor. Her
conviction was later nullified at a later posthumous retrial in which Joan was described
as a martyr and the victim of the heresy of Bishop Pierre Cauchon, who presided over the
original trial.

The charge of heresy often called for a
death by fire, and her burning at the stake was a common choice of execution. So, no, it
was not a fair trial and she was excommunicated and burned on a false charge of
heresy.