(For clarity, I have italicised French ranks and left US/British ones unformatted)
I've been reading John R. Elting's Swords Around a Throne, and one distinction of rank has confused me: I understand that the equivalent of the British/American rank of Major was the Chef de Bataillon, who commanded a battalion in battle, unlike British majors. Similarly, I understand that a Colonel commanded a Regiment, which was a formation of two or three battalions.
What I don't understand is the rank of Major, equivalent to the British/US rank of Lieutenant Colonel. In contemporary British service, a Lieutenant Colonel commanded a battalion while a full colonel commanded the administrative unit of a regiment. However, since regiments were larger combat units in the Grande Armée and battalions were commanded by a Chef de Batallion, I can't work out what the responsibilities of a Major were. Did they command depot battalions or provisional regiments, or occupy some other administrative post?
The term you are after is Capitaine-adjudant. It was his responsibility to serve the administrative needs of the battalion, which more often than not was brigaded with other units from different regiments.
A regiment is more of an administrative term where the Colonel would liaise at a brigade and divisional level. During campaign he would usually be present with the first battalion.
During battle the important command structures would be Corp commander > general de division > general de brigade > chef de battailon (colonel first battalion) > captain.
Hope that helps.