This mysteriously-appearing song, its origins unknown to me, is in the albums "The Little Mermaid and Friends" and "10 Disney Favorites: Songs from the Sea", both of which came out pretty close to each other.
From the lyrics, the song sounds like it's supposed to be sung by Ariel as she is still a mermaid and dreaming of her happily ever after with Eric. But I don't think it's a deleted song from the film, because otherwise it would've been included in one of the demo albums that have been released. Commenter Omar mentioned that the song was written by Chris Martin, not Howard Ashman, which does seem to point to this song being an original one, perhaps written for the Platinum Edition rerelease of the movie.
Anyway, it's a really pretty, wistful ballad, and showcases Jodi's lovely vocals.
There is music in the air, can you hear it?
It's in two, no, maybe three or maybe four
And I see me dressed in white
With two feet that feel so light
It's as though as they've never ever touched the floor
One dance, just you and me
Beneath the moon, beside the sea
One dance and it's happily ever after
One dance and you will see
We're not so different, you and me
Just us two, me and you
One dance
There are stars that fill the night, can you see them?
There are two, or three or gee, a million more
And I see in their light
Oh me? A dance? All right
Just to move and glide with you across the floor
One dance, just you and me
Beneath the moon, beside the sea
One dance and it's happily ever after
One dance and you will see
We're not so different, you and me
Just us two, me and you
I would change who I am
Change the sea for the sand
Just to stand with you
I would leap at the chance
For a glimpse of a glance
Of one dance with you
One dance, just you and me
Beneath the moon, beside the sea
One dance and it's happily ever after
One dance and you will see
We're not so different, you and me
Just us two, dream come true
One dance
One dance