I don't know why it's becoming popular. Maybe it's riding off its vague similarity to
Emma and
Emily? Also, the AY sound, which Esmé/Esmée has amongst English-speakers, is trendy now too--witness
Ava,
May, etc.
Esmé in particular might also be getting a boost from the boy's-names-on-girls trend, since it's the original French male spelling of the name, like
René and Aimé; see also the first known bearer of the name, Esmé Stuart/Stewart, 1st
Duke and 1st
Earl of
Lennox, who was born in
Paris and whose mother was French:
http://en.wikipedia.org/wiki/Esm%C3%A9_Stewart%2C_1st_Duke_of_Lennox. Esmée's the proper feminine form, akin to Renée and Aimée.