English and Scottish.

Jennet is shown in the Oxford Names Companion as a spelling variant of Jeanette but it also says it was used in medieval times as a diminutive [or pet name] for Jean. Jean is synonymous in Scotland with Jane for which Janet was a diminutive in the Middle Ages before becoming a given name in its own right. It is therefore possible that Jennet was an early variant of Janet or possibly a re-spelling.