Hayes' attorneys claim in the appeal that the trial judge should have granted a new trial because a witness reached the day after Hayes' conviction said he heard two guns at the time of the shooting.
That would support Hayes' claim of self-defense, but no other witnesses at the trial mentioned a second gun and none said they saw Smith with a firearm.
The appeal also contends Judge Camille Buras should have allowed testimony about Smith's 2010 arrest on a charge of domestic abuse. The lawyers claim that would have shown he could be violent when drunk.
District Attorney Leon Cannizzaro said in a statement that prosecutors proved Hayes' guilt and that Buras managed "this difficult trial fairly and impeccably."