The Oxford Names Companion, OUP "Scottish Forenames" - Donald Whyte, FGH, FSG
Notes:
French feminine form of Adrien. Adrienne is now also an established English name and a common feminine form of Adrian, from the Roman Emperor Hadrianus: "man from Hadria [or Adria]" (a town in northern Italy).
Thanks to Donald Whyte who provided much of the initial information for this site.