I like both, but I slightly prefer
Virginia.
Jean could definitely work as a nn for
Eugenia, imo. I knew a little girl named
Imogene (EYE-mah-jeen) named after her grandmother, but the grandmother was always called
Jean, so the little girl is always called
Jean (or
Jeanie), those spellings.
Gene is the masculine spelling and
Genie is what called out of a lamp when you rub it, imo. ;)