I was unable to locate a written history of the regiment.
Here are the men of the 1st Louisiana who surrendered at Appomattox as listed in the American Civil War Research Database roster.
1st LA Infantry
Organized: New Orleans, LA on 4/25/61
Mustered Out: 4/9/65 at Appomattox Court House
Jordan Ammonds, Co. B
George Barth, Co. F
Bradford A. Baugh, Co. A
Ernest Bourges, Capt., Co. B
Henry C. Bridge, Co. B
James W. Bush, Co. B
Orlando Byce, Corporal, Co. A
John Charles, Co. C
George H. Coburn, Corporal, Co. B
William Connery, Co. G
David H. Da Silva, Sergeant, Co. G
Elias Dye, Co. B
A S. Goynes, Co. B
Michael Hughes, Corporal, Co. E
Joseph Scafe Huie, Co. E
Jacob Lauff, Co. F
Louis W. McLaughlin, Capt., Co. K
Benjamin Myers, Sergeant, Co. D
M G. Parker, Sergeant, Co. B
William S. Redding, Co. I
Charles H. Thiell, Sergeant, Co. K
A C. R. Turner, Co. B
Robert P. Q. Walsh, Co. I
Surrendered on 4/9/1865 at Appomattox Court House, VA
Sources used by Historical Data Systems, Inc.:
- Index to Compiled Confederate Military Service Records
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1st Regiment, Louisiana Infantry (Nelligan's)
OVERVIEW: 1st Volunteers Infantry Regiment completed its organization in April, 1861, at New Orleans, Louisiana. Its companies were from Alexandria, New Orleans, and Shreveport. Ordered to Virginia, the unit served in the Department of Norfolk, then was assigned to A.R. Wright's, Starke's, Nicholl's, Iverson's, Stafford's, and York's Brigade, Army of Northern Virginia. It participated in the many difficult campaigns of the army from the Seven Days' Battles to Cold Harbor, marched with Early to the Shenandoah Valley, and ended the war at Appomattox. The regiment reported 214 casualties during the Seven Days' Battles, 71 at Sharpsburg, and 8 at Fredericksburg. It lost thirty-seven percent of the 125 at Chancellorsville, twenty-three percent of the 172 at Gettysburg, and twenty-five percent of the 112 at Mine Run. The 1st surrendered with only 1 officer and 18 men. The field officers were Colonels Albert C. Blanchard, Samuel R. Harrison, William R. Shivers, and W.G. Vincent; Lieutenant Colonels James Nelligan and Michael Nolan; and Majors Charles E. Cormier and J.C. Wise.
http://www.nps.gov/civilwar/search-regiments-detail.htm?regiment_id=CLA0001RI01