Are you positive as to the spelling of your ancestor's surname? I see that John C. Coulliard was in Company D, LA 6th Infantry Regiment, according to the National Archives. I then searched the Confederacy for others with that spelling, none. Then the Federal records; two, one Coulliard in Mass, another Coulliard in New York. No "Couillard" in either.
The surname interested me, as probably 30 years ago I last worked on my family history, and I remembered an ancestor on my mother's side, "Suzanne Couillandeau". Was living in Barbados in the 1700's, later in Charleston, SC. No connection between us, yet a similar spelling format.