You just have: "I will grant you that the Tribunal attempted to excommunicate her; it would seem, however, that it was invalid (and hence there was no excommunication) since it was manifestly contrary to the law."
Get off the fence.
The first trial had been conducted without reference to the pope, indeed it was carried out in defiance of St. Joan's appeal to the head of the Church. Now an appellate court constituted by the pope, after long inquiry and examination of witnesses, reversed and annulled the sentence pronounced by a local tribunal under Cauchon's presidency. The illegality of the former proceedings was made clear... (from the Catholic Encyclopedia)
I am not familiar with the medieval canon law, but it seems likely that ignoring her appeal to the Pope would have made the sentence invalid (for it was indeed illegal). That is why I made the statement that I did.