According to Art Bergeron's Book, Guide to Louisiana Confederate Units, there was a Company F in the 13th Battalion Partisan Rangers (Cavalry). It continued in operation till early February 1864, where it was renamed the 5th Louisiana Cavalry Regiment, with the addition of additional companies. Actions of the 13th inlcude activity around Delhi, Dallas Station, Lake Providance, Caledonia, and Pin Hook Louisiana. They appear to have generally operated in the Northeast Corner of Louisiana. The 5th also operated in the NE corner ot Louisiana, and in the Red River Campaign.
Review of Booth's Records shows the following:
Festiban, Richard (also Festivan, Richard), Pvt. Co. F. 13th Battn. La. (Partisan Rangers). En. July 25, 1862, Homer, La. Present on Roll for Jan. and Feb., 1863. Roll for March 1, to June 30, 1863, shows him Absent without leave.
There appears to have been a relative, a brother, that was with him:
Festiban, Benjamin (also Festivan, Benjamin), Pvt. Co. F, 13th Battn. La. (Partisan Rangers). En. July 25, 1862, Homer, La. Roll for Jan. and Feb., 1863, Absent, sick, in Hospl. Roll for March 1 to June 30, 1863, Absent without leave.
Perhaps they just got fed up and left?
Hope this helps -