Most cities with an internal dividing line are divided along a line of wealth: North London is "posher" than South London, Manhattan more glamorous than Brooklyn and so on. Paris, conversely, is divided along a frontier of the mind: the institutions of power, the state and the church, have traditionally resided on the Right Bank, whereas intellectuals have always sought refuge on the opposite side of the Seine. (No prizes for guessing what the sexier of the two is. No perfume, to my knowledge, has ever been named after the Rive Droite.)
The Rive Gauche owes its status to the Sorbonne. Not many of the old university buildings are left, and the Sorbonne is no longer considered top grade in France, but most of the elite institutions that have nestled in its shadow for centuries are still there: the SciencesPo, the ENA, alma mater of nearly every French cabinet minister since the war, and even the country's top two Grammar Schools. While on near-by Rue Gay Lussac, you can retrace the battle lines of the legendary 1968 riots.
Tip for a daytime walk: the charming Rue Mouffetard, while Rue de la Huchette, just off Place Saint Michel, is a great place for a fun night out with bars, cafes, restaurants and street performers.