Francois Villon (Karla)

According to blogger CR Ward, "Francois Villon was a French poet in the middle ages. He was born in 1431 in Paris. In 1455 Villon injured a priest and was banished from Paris. Villon was allowed to return to Paris in 1456 after being pardoned for the killing on grounds of self-defense. A year later Villon was banished again for stealing from the College of Navarre with his criminal compatriots who had formed Coquille, something akin to a small Mafia. Before leaving Paris, Villon wrote The Legacy, a tongue in cheek poem bequeathing his real and imaginary wealth to various 'deserving' people and institutions. Between times in prison he produced volumes of what are still considered by many to be the finest French lyric verse ever written.

“Ballade des pendus” translates to

        Brothers, men who live after us,
        Let not your hearts be hardened against us,
        because, if you have pity for us poor men,
        God will have more mercy toward you. " (randomwriterlythoughts.blogspot.com)

I think Capote use these specific lines from “Ballade des pendus” ("Ballade of the hanged men") in the beginning so you can have a feeling before you read the book and get an idea about what might happen the murders of the Clutter family. Also it might be what the author feels toward the murderers.  When Villon was sentence to death by being hanged he wrote the poem. I think they relate to the text is that the two murderers were sentence to death by being hanged.