English and Scottish, from the Old French Jehane/Jehanne, modern French Jeanne. Both are the feminine equivalent of John, from Hebrew "God has been gracious".
In Scotland Jean and Jane are fully interchangeable. Occasionally Jean &/or Jane have been used as a synonym for Janet, especially in early records, but this is by no means universally true [see notes for Jane] and is likely to be a localised family pet-name.
The 1841 Census for Aberdeenshire has a very significant number of occurrences of Jeane as a spelling variation for Jean [or Jane].