The Mémoires de Mme Roland is a good place to start. I know it has been translated to English though I do not know how easy it is to find a version. It may even be online for free since it is an old classic ( public domain ? ).

Memoirs from Beyond the Grave by Chateaubriand is one of my favourite book. Now he does not only deal about the Revolution, it's not even the most important part of his book but you have here the life of an aristocrat before, through and after the Revolution. Chateaubriand is also read because of his writing style, one of the best writer in French literature., father of romanticism. Like Rousseau before him, Chateaubriand's memoirs are a lot about him, about how he feels and thinks. It is not just a testimony of the events he witnessed and took part in but a testimony of his life, from the outside and the inside.

If you want a view from someone who was with the royal family, I suggest you read Mme Campan's memoirs. She was a lady-in-waiting for Marie-Antoinette and as such left us a very interesting insight of what life was at court, before and during the Revolution until 1792. A brilliant woman, who also revolutionized the French thinking on girl education. Her memoirs are available on Amazon, there is free e-book English version.

There are more of course, but those are the first I think of. Chateaubriand is what I would recommend above all the others, because it reads like a novel. The writing is brilliant, very poetic and the author is very interesting person as well.