I believe it stems from the charge that she used the Name of Jesus to form a cult.
Biblical reference:
In chapter 7 of Matthew, those people denied entry to heaven are such ones who have become famous and rich or have formed a cult in the Name of Jesus. Pretty broad charge for Joan and reversed on appeal. (too late for her)
Basic logic was:
You won’t answer our questions
You won’t say the Our Father
You refuse to deny the existance of Fairies and so forth
You use the name of Jesus to gather and hold a following (a cult)
You are therefor a heretic.
I’m sure someone that knows this better than I can provide additional info. (Or completly refute this.)