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Un geant dans la mer and Triste soiree III from the score to Marie et les naufrages by the genius, Sebastian Tellier. 
Love is Blue by Jackie Mittoo and the Soul Vendors.
Rocky Passage by Jeremiah Chiu and Marta Sofia Honer
Morris Visits Dr. Pratt from John Barry's score to The Wrong Box
Adios Muchachos from Andre Popp
Moonlight in Vermont from the great Dorothy Ashby. 
Midnight Moon by The Portland Cello Project
Dance PM by Hiroshi Yoshimura
And we hear Blind Andy Jenkins' "Floyd Collins in Sand Cave" followed by Vernon Dalhart doing the same song under the name, "The Death of Floyd Collins." We also hear Jimmy Osbourne do Andy's, "The Death of Little Kathy Fiscus."
Notes
I have a note in my years-long running list of possible story ideas that says, "event songs," but I could never remember why. Then I was reading Charles Hirschberg and Mark Zwonitzer's, Will You Miss me When I'm Gone?: The Carter Family & Their Legacy in American Music and was reminded of Andy's story (that book is great).
I also recommend the always-useful, Country Music USA, by Bill C. Malone for more on Andy and his era as well as Creating Country Music: Fabricating Authenticity by Richard A. Peterson.
If you want more about poor Floyd Collins, you could turn to Robert K. Murray and Roger W. Bruckner's, Trapped!: The Story of Floyd Collins.