The blog “Early Cajun Music” is an obvious starting place: http://earlycajunmusic.blogspot.com/?m=0
They cover music from 1928 to 1965.
YouTube channel “stbricesday” has a fun playlist of 20s-60s Cajun music: https://www.youtube.com/playlist?list=PLB5F310F1A50A7B3C
My own playlist “The Swamp” includes a variety of musical styles modern and old, and there’s a bit of classic Cajun music in the mix: https://www.youtube.com/playlist?list=PLkY8-UOMZQ0_SWp8Z2PhjEZvf089Fmoc1
A few early Cajun songs also became country music classics. “Ma Blonde Est Partié” from 1929 is better known today as “Jole Blon.” A number of country artists covered it, and it was Waylon Jennings’ very first single (with Buddy Holly on guitar). Waylon later covered “Big Mamou,” which is derived from the 1928 Cajun song “Basile Waltz” http://earlycajunmusic.blogspot.com/2016/08/le-gran-mamou-leo-soileau.html?m=1
Hank Williams’ “Jambalaya” draws from Cajun songs, and Early Cajun Music credits the 1929 Guidry Brothers recording “Le Garçon Negligent” as the earliest in this line: http://earlycajunmusic.blogspot.com/2016/09/le-garcon-negligent-guidry-brothers.html?m=1
I even remembered the cedilla on the “c.” I’ve forgotten everything else from high school French class 30+ years ago, but I somehow recalled that one.
In 1985, zydeco artist Rockin’ Sidney had a surprise hit with “Don’t Mess With My Toot Toot.” It even hit #19 on the country chart. As far as I know it’s the only zydeco song to have success on the country chart.The song draws from Cajun songs back to 1929: http://earlycajunmusic.blogspot.com/2014/10/chere-tu-tu-millers-merrymakers.html?m=1
Colombian group La Sonora Dinamita’s 1988 Spanish-language cover of the Rockin’ Sidney’s hit (as “Mi Cucu”) was very popular, too.
Cajun artists also covered early country artists. A great example is Cléoma Breaux Falcon’s 1934 cover of the Carter Family hit “I’m Thinking Tonight Of My Blue Eyes” http://earlycajunmusic.blogspot.com/2018/08/mes-yeux-bleu-cleoma-breaux-falcon.html?m=1