We're talking about Capt. Henry Louis Favrot, a noted attorney of West Baton Rouge Parish. A note to Gov. Moore can be found in his CSR, dated Mar. 16, 1861, and the flag of the "Delta Rifles" can be found today in the West Baton Rouge museum. I see nothing so far to show that this was a non-white company, but the "Delta Rifles" should be easy to research.
Capt. Favrot appears on the 1860 census as white. A quick check can be made to show that members of the Confederate "Delta Rifles" are listed on the census as white or free men of color.
If the latter holds true, this will be an authenticated instance of a non-white company in Confederate service.