I am kind of mostly looking for warfare in the Americas , where the French and English reigned and Did they have formations? How was their use of these formations? And could you give me any other tactics used by them? Thank you for reading and hopefully contributing.
I can only contribute towards the British army as I am not well read into the French army. The British army most certainly employed linear tactics when it came to battles on an open field. You can think of the big armies gathered en mass depicted in The Patriot or Waterloo (I know, 19th Century). However, they did understand and use "guerrilla tactics" against enemy armies. The establishment of Light Infantry during the Seven Years' War cemented the idea that linear warfare would not always win the battle. For those not familiar, linear warfare composed of two armies adjacent to each other and trading fire between each other until the other army broke and withdrew from the battlefield. Light Infantry worked with and against it, by using skirmishing tactics, using cover of trees, taking a knee, lying prone, and so on. The British army learned from experience in the American theatre of the Seven Years' War - the French & Indian War- to use non traditional methods while in thick brush and forest. By the time of the American War of Independence, the British army had become "Americanized" in strategy and battlefield formations of "guerrilla tactics" and open formations.
The image of the British army strolling towards their enemy and staying in perfect formation would be wrong. Military leaders knew that speed and covering distance was one of the most important factors of winning a battle. It cannot be done if the army is slowly moving down the field. They also ordered regiments or companies to be in open formation, meaning each soldier had an arm's length in between each other. The volley fire may have suffered with loosing "the wall of lead" effect, but it also meant less casualties. Battles often started at more than 200 yards away and exchanging fire at that distance would be futile as attempt to gain ground, so the armies moved closer. Open orders allowed for better terrain control if trees or posts happen to be in the way of motion. Along with open orders, leaders formed their soldiers into two ranks. Think of companies or regiments lined up, an arm's length in between each soldier, and with another line immediately behind them. They found that to be an effect way to give fire by rank or platoon if needed. Troops were ordered to hold their fire until they closed the distance between them and enemy combatants. Closing in, likely about 50 or yards, the soldiers would be ordered to fire and charge with fixed bayonets. It was about field control than utterly decimating the opposing army. Of course, holding fire until that close while under fire would prove to be a difficult task, but officers only ordered this if a bayonet charge was underway.
The formations of the army on the field did not change as much. Maintaining order on the field also meant to have control and steadiness of their own troops. The standard structure included the most senior company to be on the right and the most junior on the left. This began with the Colonel’s company, Lieutenant-Colonel’s company, Major’s company, and then the captains. This resulted in all of the most senior officers being concentrated on the right of the battalion and so some nations overcame this by a tactical organisation which interspersed junior and senior companies along the line. Flank companies formed at the ends. Flank companies consisted of the Light Infantry company and the Grenadier company. To lay the formation out it would look like: Flank, 8th, 7th, 6th, 5th, 4th, 3rd, 2nd, 1st, Flank. Two exceptions though, often times the regiments detached their flank companies which formed their own battalions, ie. Light Infantry Battalion or Grenadier battalion, as well as the Flank companies did mean lesser or more senior officers in the line. 1st company would be the Colonel's, not the Flank at the end.
I should add that cavalry fell into a similar suit but their tactics and purpose differed than the infantry units. However, by the AWI, they adopted the two rank and open files as well. I know less of the cavalry and cannot say for sure the lay out of squadrons on the field.
Alex Burns, "How Close Ranged were Mid-Eighteenth-Century Firefights?" Kabinettskriege, Jan 31, 2018. Link.
Alex Burns, "How Often did Regular Troops Fight as "Skirmishers" in the Mid-Eighteenth Century?" Kabinettskriege, Feb 28, 2018. Link.
Bennett Cuthbertson, Cuthbertson's System, for the complete interior management and œconomy of a Battalion of Infantry.
Matthew Spring, With Zeal and Bayonets Only.