Adelaide, Arabella, Georgette, Freya, Fleur, Jemima, Lucinda, Lucianna,
Matilda, Poppy, Saffron, Tamasin (not Tamsin), Tansy, Willow

Georgette and Matilda sound really really old fashioned to me.
Poppy sounds like something you call an old man. Tamasin is pretty,
although I've never heard it. Fleur definitely doesn't go with
May, and folks might have a hard time pronouncing it (do they
say it with the French vowel -- not in English -- or not?).
Lucinda May, Arabella May, Tamasin May all sound good in combination.
I don't think May is a cheesy middle name, even for a May baby.

FWIW,
Emily