I'm sure you can find a number of sources on this answer, but I'll refer to Marcel Gauchet's "Left and Right" from Realms of Memory: Conflicts and Divisions as the best source for a succinct answer.

The short end of the origin of "left" and "right", is that it comes from the relative seating one took in the French National Assembly shortly after the French Revolution broke out in 1789. Members of the National Assembly who supported the Ancien Regime sat on the right, while members who were in favor of the revolutionary cause sat on the left. At the time, the idea that "parties" (or "clubs") were fractious and divisive held a lot of currency, and so general labels of "left" and "right" were used to describe the two groups in the press.

Generally speaking, you would find proto-socialists (socialism wasn't an articulated idea at the time, or at least anything like we understand it now, so it wouldn't be fair to call them socialists), liberals on the "left" side of the assembly. On the right, you would find petty nobles, ultra-royalists, landowners and the like (the groups of people with the most interest in defending the status quo).