I don't think
Jean was ever popular enough to need freshening - certainly not where I live. I'd be happy to meet a young
Jean, and happy to use it myself.
Jeane makes about as much sense as Jille or Ruthe. Not a lot. If you live where there are lots of boys named
Jean with the French pronunciation, then
Jeanne would be useful. But if you don't plan to use the French pronunciation, then why confuse the issue?