The title "Annunciation carol" may be misleading, since a number of these carols have more specific titles.
One from the Basque country is "The Angel Gabriel From Heaven Came," translated into English by Sabine Baring Gould.
Text and midi in the Cyberhymnal: www.cyberhymnal.org/htm/a/g/f/agfhcame.htm
Angel Gabriel
Three others are given in the Cyberhymnal, but have even less relationship to the Bas Quercy region.