"I believe I have read somewhere that Co C became a part of the 7th during the Battle of Franklin"

Ms. Debbie, your ancestor was in Company C of the 6th Regiment Mississippi Infantry. They were in a different division and corps from the 7th regiment during that horrible battle. There was no consolidation of the two regiments. The 6th Regiment was occasionally reffered to as the 7th early in the war and this looks like an error on the part of the person who told you this or who wrote it.

The best way to follow your ancestor's career in the army is to get his service record and any pension application he may have filled out. Then follow the history of his regiment and compare its actions to where he was according to the muster rolls on his service records. Pension applications sometimes include specific information but unless he left behind diaries or letters etc. that is the best way.