From the Oxford Dictionary of English Christian Names, 3rd edition
"Esmé(m, f) the first occurence of this name seems to be Esmé Stuart (1542-83), bth Seigneur d'Aubigny and afterwards Duke of Lennox, cosuing of James VI of Scotland, whose mother was French. His name, which is not found earlir in the family, and which was borne by his son and his grandson, was sometimes spelt Aymie, and it is possible that it it really the fairly common French name Aimé (see Amyas). The name spread from the Stuarts to other Scottish families and eventually to England. It is now sometimes given to girls, probably from confusion with the old name Ismay."
(Ismay was a female name used during the middle ages, and is of obscure etymology.)
So Esmé seems to be the traditional spelling in Britain for both girls and boys. Esmée comes from believing it to be a French name. In fact in either form it has only been used in France very recently (Esmée only since 2000, according to registers), having migrated from English-speaking countries.
Terry Pratchett fans will undoubtedly nickname her Granny or Weatherwax.