There are many songs that contain those syllable. Sinc you asked about a "carol" you are probably thinking of "Deck the Hall," which is generally sung at Christmas.
Deck the Halls
Deck the halls
Deck the halls
The carol is 'Deck The Halls', but the tune was originally a Welsh folk song. Deck the halls with boughs of holly, Fa-la-la-la-la-la-la-la-la, 'Tis the season to be jolly, Fa-la-la-la-la-la-la-la-la, Don we now our gay apparel, Fa-la-la-la-la-la-la-la-la, Sing the ancient Yuletide carol, Fa-la-la-la-la-la-la-la-la!
Deck the halls.
the answer is deck the halls (with boughs of holly)
deck the halls it goes "deck the halls with boughs of holly fa lalalalalalalala tis the season to be jolly falalalalalalalala don we now our gay appearel, falalafalalalalala troll the ancient yule tide carol falalalalalalalala"
Deck the Halls, a traditional Christmas Carol.
la-ti-la-sol-fa-fa-la-la-sol-fa-mi-la-sol-la-do-do-ti-ti-la-la-la-ti-la-sol-fa-fa-fa-fa-sol-la-ti-la-ti-la-fa-sol-sol-ti-la-sol-fa............
Deck the halls with boughs of holly,Fa la la la la, la la la la.Tis the season to be jolly,Fa la la la la, la la la la.Don we now our gay apparel,Fa la la, la la la, la la la.Troll the ancient Yule tide carol,Fa la la la la, la la la la.See the blazing Yule before us,Fa la la la la, la la la la.Strike the harp and join the chorus.Fa la la la la, la la la la.Follow me in merry measure,Fa la la la la, la la la la.While I tell of Yule tide treasure,Fa la la la la, la la la la.Fast away the old year passes,Fa la la la la, la la la la.Hail the new, ye lads and lasses,Fa la la la la, la la la la.Sing we joyous, all together,Fa la la la la, la la la la.Heedless of the wind and weather,Fa la la la la, la la la la.
do do re do fa mi do do re do sol fa do do do la fa fa mi re tib tib la fa sol fa do do re do fa mi do do re do sol fa do do do la fa fa mi re tib tib la fa sol fa
So so so dodo mi re mi fami re mi faso fa mi fa somi fa so la lado ti la soso la so fala so fa mi