‘Genevieve’ was probably Jenny Edwards, the daughter of a school matron in Christ’s Hospital.  Coleridge was in the sick ward for most of 1789, when he would have seen her regularly.

Maid of my Love, sweet Genevieve!
In Beauty's light you glide along:
Your eye is like the star of eve,
And sweet your Voice, as Seraph's song.
 
Yet not your heavenly Beauty gives
This heart with passion soft to glow:
Within your soul a Voice there lives―
It bids you hear the tale of Woe.

When sinking low the Suff’rer wan
Beholds no hand outstretcht to save,
Fair, as the bosom of the Swan
That rises graceful o’er the wave,
I’ve seen your breast with pity heave,
And therefore love I you, sweet Genevieve!