I know that Frankenstein's family were rich enough for him to take frequent vacations, but were they titled nobility? And if they were what title or titles did they hold?
I think the closest you come to an answer is in the first paragraph of chapter I (of the Project Gutenberg edition)
I am by birth a Genevese, and my family is one of the most distinguished of that republic. My ancestors had been for many years counsellors and syndics, and my father had filled several public situations with honour and reputation. He was respected by all who knew him for his integrity and indefatigable attention to public business. He passed his younger days perpetually occupied by the affairs of his country; a variety of circumstances had prevented his marrying early, nor was it until the decline of life that he became a husband and the father of a family.
The Wikipedia article on Swiss nobility makes it clear that at the time of writing, the concept of titled nobility did not play a big role in the Republic of Geneva, at least not when compared with England, France, or Italy. I do not know know if "ancestors had been for many years counsellors and syndics, and my father had filled several public situations with honour and reputation" counts as qualifying for the aristocracy. If your question is really "was his name von Frankenstein?", I think the answer is "probably not; there is no direct evidence in the book". Otherwise, I think the answer depends on your precise understanding of the word "aristocracy".