Yup, just as I suspected from your description of the song, this song jumps octaves between the verse and the chorus. I'd say the verse starts on the D# below Middle C and the chorus starts on the D# above Middle C. I feel that their tonics are similarly 1 octave apart from each other.
I'd say the verse starts on F#, actually, although I suppose you mean the extra note for the extra syllable in the second verse. Low it is, then. That is quite low for the verses!
Edit: I was mistaken! Back when I made this topic, I thought that men and women used the same registers, with bass being the lowest, then alto, then soprano, and tenor being the highest human voice range. This is incorrect, though: tenor is actually a little bit lower than alto! Bass and tenor both sing an octave lower than I thought. Taking that into consideration, starting the chorus on D# above middle C (D#4 in the Young system, D#' in the Helmholtz system), the choruses are actually very high, and the verses aren't low!