Hundreds of years ago the world carol meant a round dance, a ring
of people, a circle of pillars.

Old French: Carole Provincial: corola Latin: corolla, garland

A few associate the word with chorus. I suspect that Christmas carol
go its name as the chorus sang their songs while formed in circles
or semicircles, and the name just transferred over from the older
ring dance to the songs themselves.

Happy Holidays and Merry Christmas!