I think none of the previous answers really got it right, though a few came close. First of all, Joan of Arc was not a general. Officially, she acted more as a standard-bearer. As for being a "de facto" general -- Joan's gift for military strategy was vastly overstated during the Trial of Rehabilitation (even more outrageously rigged than the Trial of Condemnation, as the Valois king desperately needed to legitimize himself through legitimizing Joan) and by the flag-waivers making the case to Rome for Joan's canonization in the heyday of nationalism in the early 20th century.
What Joan was -- rather than a military leader per se -- was a fiery populist and a competent agitator, who pioneered the use of religion to justify a political cause.
The Catholic Church tried Joan of Arc a total of 3 times -- twice during her life and once posthumously. It confirmed the divine origin of her visions in the first trial, condemned her for heresy in the second, and rehabilitated her in the third. Each of those trials was mostly a political affair, with the church leaders acting as the agents of the Dauphin or the English, respectively. The *official* reason for her condemnation was, first and foremost, that she rejected the authority of the Church as the sole source of information regarding G-d's will (she persisted in relying on her visions instead), and that she cross-dressed. The cross-dressing was a *pretext* for finally executing her (in fact, her dress was taken away from her while she slept, and she was given a man's clothes in order to force her to "relapse"); but her act of overstepping the boundaries of her gender wasn't the real reason behind her fate.
She also was never convicted of witchcraft. Under canonical law, a virgin could not be a witch, and a physician confirmed Joan's virginity to the court. Some men were dispatched with orders to rape Joan in order to facilitate her conviction of witchcraft -- standard procedure in ecclesiastical trials where the accused happened to be a virgin -- but were unable to perform the act (prompting speculation among historians about Joan's anatomy and even her gender). With this impediment to the witchcraft conviction remaining, Joan was convicted only of heresy.