The following is contained in the Andrew Booth Compendium on Louisiana Soldiers (Google "Andrew Booth and Louisiana"):

Grillett, Spir, Pvt. Co. D., 3rd La. Inf. En. May 17, 1861, New Orleans, La. Present on Rolls to June 30, 1861. Roll for July and Aug., 1861, Absent. Attendant on sick at Mt. Vernon. Rolls from Sept., 1861, to Dec., 1861, Present. Rolls from May, 1862, to Feb., 1863, Present. Federal Rolls of Prisoners of War, Captured and paroled Vicksburg, Miss., July 4, 1863.

McWilliams, J. C., Pvt. Co. C, 6th La. Cav. En. April 6, 1862, Monroe, La. Present on Rolls to Dec., 1862. Roll Jan. and Feb., 1863, Absent, sick, in Hospl. Roll of Prisoners of War, C. S. A., Paroled Natchitoches, La., June 19, 1865. Res. Bossier Par., La.

McWilliams, John, Pvt. Co. E, Stewart's Cav. Roll of Prisoners of War, C. S. A., Paroled Alexandria, La., June 31, 1865. Res. Rapides Par., La.

McWilliams, John, Pvt. Co. E, Cons. Cres. Regt. La. Inf. On Roll of Prisoners of War, C. S. A., Paroled Alexandria, La., June 31, 1865. Res. Rapides Par., La.

McWilliams, John, Pvt. Co. I, Cons. Cres. Regt. La. Inf. En. Camp Pratt, Sept. 25, 1862. Roll Jan. and Feb., 1864, Absent, detailed in Alexandria on Provost Guard, Feb. 13, 1864. On Roll of Prisoners of War, C. S. A. Paroled Alexandria, La., June 3, 1865. Res. Rapides Par., La.

It would seem likely that the first two are your ancestors, but Booth does list 4 J. or John McWilliams. The Bossier Parish residence and the J. C. do strongly suggest that the first is your ancestor. You would need to confirm in other ways. I will see if Footnote.com or the National Park Service Soldiers and Sailors registry has any information. You can get to the Booth compendium on the Louisiana page of the USgenweb.

Hope this helps.

Don Parker