I speak Irish (not my native language, though), and there's a bunch of them. Here's some of the more traditional, 'sean-nós' songs:
Amhrán Mhúinse - https://www.youtube.com/watch?v=By0QM8mlr28 (English lyrics are in the description) - This is probably my favorite of all Irish sean-nós songs. It's super haunting, and made even sadder by the fact the woman who wrote the song didn't get her wish to be buried in her home area.
Coilín Phádraig Shéamuis - https://www.youtube.com/watch?v=EOjSOAxN9Wg -- Typical song about immigration, quite melancholic.
Also, Iarla Ó Lionard does quite a lot of good work in the sean-nós tradition (he was heard on the film Brooklyn); here's one of my favorites by him - https://www.youtube.com/watch?v=35U1sOOjdDg
FInally, it's hard not to mention Seosamh Ó hÉanaí/Joe Heaney/Joe Éinniú, a native speaker from the Galway Gaeltacht - https://www.youtube.com/watch?v=zrSL3YtzP_w
And, for some newer works in the language that I enjoy
An Cailín Álainn - https://www.youtube.com/watch?v=n5l82gO7tuw
Pócaí Folamh is Cloigeann Tinn - https://www.youtube.com/watch?v=d0L54BJFRnw
Siar go Conamara - https://www.youtube.com/watch?v=7tywACdkAgc
All of these songs are sung by natives, which, sadly, is getting less and less common as the native speaking areas dwindle and as summer camps get millions of views translating the latest English language hit for summer school kids with awful pronunciation to sing.