A real insider in Paris need set out with no more equipment than a bunch of Metro tickets (a carnet of 10 currently costs 22 francs, or about $3) and a Plan Taride, the neat red map that divides Paris into its 20 arrondissements. The arrangement of these wards may seem arbitrary, but not once you know that Napoleon laid them out in a snail's spiral, starting with the first arrondissement at the Louvre and winding outward.
A single metro ticket is valid for a journey anywhere within these city limits, and the same tickets work on the buses, too, though a longer bus journey can demand more than one. But serendipity does better in the open air. Almost more than any other city, Paris exists to be walked in. The distances are never insuperable, so it's worth thinking twice before diving underground.
If you are taking the Metro, get out at Republique to explore the Canal Saint Martin. The Rue du Bac is one of the stations serving the Faubourg Saint Germain. The natives in this part of the world are on the stiff side of genteel, but don't let that stop you, in the daytime, from pushing open the massive doors onto a different world. Inside 102 Rue de Grenelle, for instance, it feels like a country estate: The single tree in the cobbled courtyard is ringed with two-story stables.
At Le Train Bleu (Metro Gare de Lyon), prices start at around 200 francs a head, depending on the choice of wine. Their 1962 Chateau Soutard, a Saint-Emilion at 180 francs a bottle, is a bargain, and the 1971 Chateau Bougcaut is also recommended. For reservations, call 343-09-06, though the size of the restaurant is such that there's usually an extra table somewhere among the hurly-burly. Unlike most top Paris establisments, Le Train Bleu is open on Saturday and Sunday--and thrives on it.