Question

How did the French and Indian War, in 1763, contribute to the writing of the Declaration of Independence?

Answer 1

The entire situation with the colonies revolting from British control wouldn't have happened without the Seven Years War (of which the section happening in the North American colonies is called the "French and Indian War"). 

The British only raised taxes, which is the thing that first upset the American Colonies, to pay down the debt from fighting that war. 
The British wouldn't have been considering allowing the Catholic settlers from Canada to move into the Ohio Valley and to keep those from the American Colonies out if they hadn't won the war, since Canada would still have been French. 
The American colonists would have had less grievances with the British for the way that the leadership of the British armies messed up in the Colonies if the war hadn't happened. 
The American colonists wouldn't have had as many experienced combatants and leaders (Washington being a huge one that learned his skill in war fighting for the British) without the earlier war taking place.