I think it should be
We live along the river
I keep answer with "river" too. But isn't "river" actually แม่น้ำ? Or is "water" used as a short way to say "river" as well?
The audio is wrong. It pronounces "live" with the long i sound as in "live music" but it should be the short i sound as in "I live here".
Oh it's been fixed!
It should also work with "alongside" and probably with "by" too.