David, this is a question that deserves more than a response of one or two paragraphs. We are talking about the possibility of developing a course on the history of conservatism and libertarianism that would flesh this out in much more detail, but that is months down the road.
As you note, these words originally referred to supporters (left) and opponents (right) of the French Revolution and its legacy. They retained those meanings in Europe to a great extent throughout the 19th century and the early 20th century. Now that the French Revolution enjoys nearly universal approbation in Europe, “left” is usually employed to refer to social and economic egalitarianism, and “right” is used to refer to anyone who objects to those things.
In his essay “Left and Right,” Murray Rothbard argued that a better way to view the spectrum is that “left” is anti-State, and “right” is pro-State. This was his attempt to woo New Left opponents of the Vietnam War in the late 1960s, but the argument never really caught on in broader public discourse. Today in the U.S. the terms mean pretty much what they mean in Europe.
Most libertarians today will argue that “left” and “right,” or at least “right,” aren’t really that useful in describing one’s political program. “Left” might mean something definite, but “right” is employed to refer to everyone from libertarians and classical liberals to Buchananite populists to divine-right monarchists to neo-Nazis. It obscures more than it illuminates.