looking at this cameo, which is an antique cameo ring, I am not so sure the subject is Joan of Arc - it might be 'Athena' a greek goddess from Ancient Greek mythology who was a very popular cameo subject although, with that demure face and still energetic half smile, she looks more like the Mona Lisa!
Joan of Arc or helmet clad Greek warrior goddess Athene Parthenos better known as Athena or "Minerva" to the Romans, it is a lovely piece. The style of helmet she is wearing would provide regional clues. Is it a Greek, French or Roman helmet?