Carrington was responsible for raising a lot of the Ohio and Indiana regiments that fought in the battle of Franklin.
Carrington's second wife was Fannie Courtney-She wrote about the battle of Franklin.
One connection is that Carrington had organized the first 26 Ohio regiments (Source).
Of these regiments a fair number fought in the Battle of Franklin, e.g. the 9th, 13th, 15th, 20th and 26th Ohio, just to name a few.
Henry Carrington’s second wife, Frances “Fannie” Courtney, lived in Franklin and was an eye witness to the Battle of Franklin. She wrote a report to the Sanitary Commission about the battle. She also had a brother and cousin serving with Nathan Bedford Forrest.
Carrington was commissioned Colonel of the new 18th U.S. Infantry that he organized in May 1861. It was transferred to the Twenty-third Corps and fought under Gen. Schofield at the Battle of Franklin.
Carrington also had connections to the Battle of Franklin by marrying Frances Courtney of Franklin, who was the widow of George Grummond, posted in Franklin to serve as Provost Marshal. Grummond died serving in the 18th U.S. Infantry under the command of Carrington.