Ok. St Jeanne is one of my all time favorite saints. First of all, she was a peasant from Lorraine, and her real last name, the name of her father, was not "d'Arc" but just plain "Darc." (They changed it to "d'Arc" after she was ennobled by Charles VII for her services to France.)
She was not killed because of sexism but because she was an enemy of the English, whose prisoner she was. The bishop who condemned her and presided at the mock trial, Bishop Cauchon, whose name was henceforth used to call pigs, was in the pay of the English, and his treatment of Jeanne COMPLETELY contravened ecclesiastical (Roman Church) law. Jeanne appealed "to God and to our Holy Father the Pope" which meant she should have been immediately sent into a convent in the care of nuns and questioned by the Holy See directly. It was her right under church law.
However, the evil Cauchon and his English masters insisted that she be guarded by coarse English soldiers. She wanted to put on a dress but was afraid the guards would rape her so she kept on the male attire. They did this to her on purpose so they could accuse her of being a relapsed heretic. She denied hearing her saintly voices in order to get away from those men, but when they tried to molest her, she retracted her recantation, realizing that she had betrayed her voices, and so was considered "relapsed."
King Charles VII, at the urging of Jeanne's feisty mother, took the case to Rome 20 years later and Jeanne's innocence was officially declared. It had all been completely contrary to church law to begin with and many bishops, priests and faithful were appalled by it. And rightly so, it was a travesty. Jeanne is the Patroness of France with St Therese of Lisieux. She is also Patroness of Soldiers.