You could start by reading wikipedia and looking at their primary sources. They're usually pretty good. Also just google for articles and journals about the war and 18th century culture. A major one would definitely be the ancien régime as that was France's governing system at the time.
Are you writing about the events that led to the war or about the war? Because the French Revolution happened in 1789-1799 and your dates (1775-1783) coincide with the American revolutionary war.
Also I don't think anyone here can give you a conclusive answer that takes into consideration all the social, political, religious and cultural events that led to the French Revolution. It was a pretty significant war. If you're going to write a story about a historical event I'm afraid you're going to have to study it yourself.