Why fight? The French wanted to claim the Ohio River Valley for trade (mostly fur trade) expanding, and transporting (goods and people). The River brought great values of such. They also kept their alliance with the Native Americans which left them more advanced than the British, having an alliance would determine which side would win the war. Alliances: Huron, Delaware, Shawnees Lenape, Ojibwa, Ottawa, and the Algonquin. The French relied on their alliances. Strategies: They used European Native American fighting style to spread out troops to attack at different angles. Victories: The French started the war when French Fur traders destroy British post at Fort William Henry in 1750. Then, in 1754 General Washington surrenders at Fort Necessity. About a year later General Braddock is killed in battle near Fort Duquense, and the British forced out 6,000 Acadians. Lastly, in 1757 the French faced faced their last victory early in the war at Fort William Henry. They still stood a chance to defeat the British at this point. At least until a turn of events that become major British victory, and a huge downfall for the French a couple years later.
British
Why fight? The British fought the French to take over the Ohio River Valley for trade, expanding their land, and transportation. Mainly, for the same reasons as the French, due to the easy and convenient accessibility and resources the River brought. The British also lost their allies earlier on because the Indians didn't like their decisions and weren't treating them with loyalty. Alliances: Iroquois, Catawba, and the Cherokee. The British relied on their alliances. Strategies: In battle used civilized formation to approach their enemy to them seem more threatening and intimidating. In order to form allies they made peace with the Indians by adapting to cultural practices such as painting their faces for sometime. Victories: In 1759 the British face their first victory when William Pitt becomes Secretary of State, and in 1759 takes a turn of events. The Battle of Quebec results in the Montreal surrender in 1960 (the French surrender to the British). In between their winning streak the Indians rebel on the British and French messing up their alliances. (More is about this rebellion is described under Indian victories down below.) However, the rebellion was not a great success for the Indians, so they surrender. In 1763 the Treaty of Paris ends the war, in which the final victory goes to the British.
Indians
Why fight? The Indians didn't want to lose any more land (already feeling squished) they only wanted to keep their own land. But both British and French pushed them off there land. So they had to pick a side they wanted to have allies with but wanted the side they picked to be the side that is loyal to them. The French were chose by the native tribes because of their trading before the situation. The French showed loyalty and respect when François-Marie Le Marchand de Lignery painted his face and dressed like the Indians. Alliances: Different Indian tribes split up between both the French and British for sometime. The Indians didn't rely on their alliances much because they had tricked the British and France into becoming allies planning to rebel against the French and British later in the war, because they didn't want their land taken over. Strategies: They ducked behind trees and bushes to fire at their enemies for surprise attack and used guerrilla warfare. Also, they had prior knowledge of their geography in which they were able to adapt their strategies for war. They used that advantage by knowing escape routes through the Ohio River and, the using Appalachian Mountains for protection. Victories: In 1763 the Indians had won a victory, but this victory was towards the end of the war. It was called the Pontiac's Rebellion. However, when they broke alliances rebelling on the British and French it weakened them, causing the Indians to surrender without an alliance to back them up. This left the war between the French and British, without Indian any Indian alliances.