In Reflections on the Revolution in France, Edmund Burke argues on two fronts. First, he claims that the French Revolutionaries, by turning their backs on their historical institutions, particularly the Church, the nobility, and the monarchy (the "publick ornament" of French society,) are presuming the ability to create a new society, from scratch. Burke believes strongly that any such enterprise is doomed to failure and anarchy. By trying to base their revolution on universal "natural rights," which Burke characterizes as the invention of philosophers such as Jean-Jacques Rousseau, the "insane Socrates of the National Assembly," the French Revolutionaries opened the door for greedy speculators and ambitious would-be tyrants.
Secondly, Burke was concerned that radicals in his own country were also asserting the same principles as the French Revolutionaries. Reflections on the Revolution in France was written in response to a speech given by a radical Dissenting minister, Richard Price, in which Price compared the ideals of the French Revolution to those of England's Glorious Revolution a century earlier. Burke admits no such comparison, claiming that the revolution of 1688 was an attempt to reassert ancient English rights, not to usher in new, abstract rights posited by philosophers. The revolution simply reclaimed Englishmen's "entailed inheritance derived to us from our forefathers . . . without any reference whatever to any other more general or prior right." As such, it was a legitimate revolution, because it was essentially conservative. It preserved the rights and institutions of the unwritten English constitution rather than claiming to create new rights.
It is worth noting that Burke held the same view of the American Revolution. He frequently spoke out in support of the colonies, who he saw as simply asserting their inherited rights as Englishmen.