One of the principal reasons behind the hostility between France and England in the mid-18thC. is the way in which each country viewed the territory held by the French, which included almost the entire middle part of what is now the United States.  Whereas the French generally wanted to exploit the area's natural resources--beaver skins, for example, which were highly valued--but had no desire to settle the land on a large scale, the English wanted not only to exploit natural resources but also, and more important, to settle the territory, particularly what is known as The Ohio Territory, and create permanent settlements and to farm the land.

As English moved west into French territory, especially during the 1750's, the French, not having enough troops in the area to discourage the English, encouraged their Indian allies to resist the encroachment of the English.  Battles between English settlers and Indians became increasingly common--usually with the English suffering most--and the war became not a war for the right to use territory but a war to occupy and improve territory.

From the English perspective, then, it became ridiculous to think that France, which had few settlers but many explorers in the area, could stand in the way of Engand's westward expansion.  The French and Indian War, therefore, became an essential struggle to eject the French from the entire North American continent.  An unfortunate part of this struggle was the killing of thousands of American Indians, particularly those who sided with France.  Even Indian allies of the English were ultimately seen as impeding English progress westward and were displaced on a routine basis even after the war concluded with England out of North America.

The French and Indian War was a piece of a much larger war between Great Britain and many German states on the one hand and France, Spain, Russia and the Habsburg Empire on the other.  The French and Indian War itself (the part of the war that was in North America) only involved Britain, France, and their respective Indian allies.

The French and Indian War came about because both France and Britain claimed parts of North America.  The French were putting forts in some of these parts of the continent.  The British (and remember, the American colonies were British at this point) were worried about this.  The war started when British colonists went out to build a fort in disputed territory and found a French fort there already.  This led to a battle which then led to the war.