Might be Bonnie Blue Eyes, recorded by Joe Falcon and Cleoma Breaux Falcon for Decca Records in Dallas, February 21, 1937. Same Decca session when they recorded Lulu's Back in Town, Hand Me Down My Walking Cane, Le Nouveau Lafayette, and It's a Sin to Tell a Lie. From Tony Russell, Country Music Records: A Discography, 1921-1942.

The Decca recordings by Joe and Cleoma are mostly unissued on any compilations. There are about 20+ songs that most likely very few people have ever heard.

Is this the same song? It's done live at the Brandywine Festival in July 1977.

http://www.npmusic.org/Balfa_Brothers%20_Dont_Cry_My_Beautiful_Blue_Eyes.mp3

On this JSP 4-CD compilation there is the Hackberry Ramblers' version. From the notes, it was recorded in New-Orleans in 1935. I can email it to you if you need it (but they sing it in English).

http://www.amazon.com/CAJUN-Rare-Authentic-Various-Artists/dp/B001FY7BD4

Cristian, I would be interested in that one, but alas i haven't got the time to dive further into the matter right now: quite busy with gigs & studio stuff.
- I have the Eddie Lejeune CD, but i am mostly interested in old time country versions like the Carter Family one. Thanks, Nout

Here's the Cleoma Falcon version:

http://www.npmusic.org/Joe_Falcon_Cleoma_Breaux_Falcon_Bonnie_Blue_Eyes.mp3