Does khoác mean something on its own relevant to áo?
It can be used as a verb meaning to put something over your shoulder. It is normally used for coat, backpack, raincoat etc. - something you wear on your shoulder and behind your back.
khoác áo = put on a coat
khoác ba lô = put on a backpack
Tiếng Pháp = anorak (it sounds very similar to me)
Indeed. But it's a coincidence. Anorak is from Greenlandic annoraaq. Áo khoác is an indigenous word in Vietnamese and literally means ‘upper garment for putting over the shoulder’.
Written with music notes,
this is exactly what he says or "sings":
a - o kho-ac