Video shows two men walking on the sidewalk to their hotel on Bienville Street when they're attacked from behind by four suspects.
In the video, one of the men hits Curran in the head, before putting him in a headlock while dragging him down to the ground and holding him there.
He suffered a fractured nose and had stitches in his face, the relative said.
On Monday, the man in charge of the police district that patrols the French Quarter and Central Business District said total robberies and overall crime there are down roughly 40 percent year-to-date. The assailant continues to punch Curran as he struggles to drag Curran to the ground. The attacker quickly rummages through the motionless victim's pockets as two other men run up and appear to help rob both victims.
State law defines second-degree robbery as taking "anything of value" from someone and inflicting "serious bodily injury".
One came back briefly and lifted the second tourist up off the ground for a moment, revealing what appeared to be a pool of blood on the sidewalk.
Curran then crawls over to Byrne, who appears to heave his right shoulder with each breath, but otherwise remains limp.
Authorities told CBS Boston that police arrived on the scene about two minutes later and that 50 NOPD officers were patrolling the French Quarter that night.
Police say the two victims were transported to a local hospital after the incident was reported.