It's really quite likely to find family members who have the same name. There's no law to prevent anyone from naming a son after a favorite uncle or brother or cousin. I did, and one of my cousins did as well, so today there are at least three living family members with the same name. However confusing it may be to family researchers, it's just common practice among Southern families.
This may be the case with your family. Your Francis M. Wise appears on the 1860 census of Spalding County, post office listed as Griffin, Ga., age 43. He and his wife Martha are in household 352 which includes eleven children. They are found on page 208 of the manuscript census, although the census taker marked it as page 50.
Francis M. Wise (the soldier) appears on the 1860 census of Butts County in Iron Spring District, age 24. He and his wife Mary and an infant are in household 336 on page 50 of the manuscript census. The page number is the same as recorded by the census taker.
Also reported on this page are households of Green S. Wise, age 54, Augustus Wise, age 52, and Anderson W. Wise, age 26.
You know much more this family than myself, and it would confuse matters further for me to guess about F. M. Wise's brothers. However, the census lists William S. Wise and the oldest child (age 22) living with Martha and Francis Marion Wise's household. The child nearest to 'Rody' is listed as age 16 (born about 1844/45), but the name is given as 'Roda'. This child is female, which may explain why we can't locate a military record in that name.
On the 1850 census schedule for Butts County, the little girl's name is reported as 'Rhody', age 5.
If you will offer a purpose for wanting the CMSR for Francis M. Wise, 30th Georgia Regiment, I can offer an opinion as to how useful it may be to you.