This is something that has been in my mind for some time. I'm asking about armies such as the British, French, or United States in a time range from the American and French Revolutions up to the American Civil War.
How would these regiments actually march in a battle? I've heard of the French Column, or the two ranks of the British line. But one thing that has bothered me is that most of these regiments are organized into companies, with chains of command.
How would these play a part in battle? Would men form up in companies and march in several blocks, or would it be just a single large block (or column) of men, and companies existing mainly for accountability purposes?
This differed between time period, nation, battlefield, commander. Between the Seven Years War and the Revolution, there was a lot of discussion on how soldiers should march. Before this, soldiers would generally move by line and in battalions. The regiment wasn't the smallest unit on the battlefield and companies are more of a logistical separation at this time period.
So depending on what was needed, a French line battalion would move in both line and column; column for easy movement or in line for easy engagement.
During the Revolution, a new concept was created, the mixed order (see this link of me discussing it during the Napoleonic AMA). The concept was to have untrained sans coulette March in column and ready for a bayonet attack while supported by trained regulars in line formation. Napoleon would have his commanders use it during battle but away from the Emperor, formation would depend on the battlefield.
Generally, movement depends on the terrain. Yes Britain preferred the Line and France became famous for the column, but in general it's a locational thing.