The Mishnah B’rurah (53 s.k. 82) says it is mutar unless the song is meyuchad specifically for mass. Therefore if it is a song that is sung both outside the church as well (l’havdil, parallel to the tunes chazzanim use for l’cha dodi and mimkomcha etc., not the actual nusach) then it is fine. He is quoting a Bach (Shu”t Bach haYeshanim 127) and though I don’t have one offhand I distinctly remember that the Bach’s reason that such a song is problematic is because of uv’chukoseihem lo seileichu, (which applies to anything meyuchad for avodah zara, not because of any inherent tumah) which does not apply to regular songs of non Jews specifically because of what I mentioned above that music is a chochmah, and he quotes the gemara in Avodah Zara that “lav minayhu gamrinan”, i.e. the goy didn’t “make it up”, he just thought of it.
The same halacha is found in Birkei Yosef of the Chida, if I remember correctly it’s in 560 by the g’zeirah not to listen to music after the churban.