salamanda - Jane/Jayne were both registered as surnames, before being used as first names. Jane came first, with the earliest existing record of it as a surname was in 1509. The earliest existing record of Jayne being used as a surname was 1528.
The earliest that Jane/Jayne were recorded as baptismal (first) names was in the early 17th century, as part of the Puritan movement, because the surname derived from Jans (a Medieval England form of John) so the Puritans recognized the potential for Jane/Jayne to be a feminine form of John.
Therefore, from the records that have survived the centuries, both spellings appear to have started being used as first names around the same time.
I suppose for arguments sake, you could say Jane is the original spelling, as it was the first spelling for the surname. However, as far as the first name goes, I would say neither spelling was first.
I've probably bored you to tears with the history lesson, I apologize!