In the movie "Something's Got to Give" with Jack Nicholson and Diane Keaton, they end up meeting at a restaurant in Paris. The restaurant really exists in Paris (not on a movie lot), and is called the Grand Colbert. The restaurant is also an historical monument, and it is a great place to eat fabulous French food. If you are craving any of the French classics whether a huge fruits de mer platter of seafood, a steak tartare, or foie gras, then come here for dinner and finish with profiteroles (ice cream puffs) or a tarte tatin (apple tart) for dessert. You can stop in just for a hot chocolate (done the old-fashioned, non-machined, non-packaged way) as a respite from strolling the area's shops, or better yet have lunch here with the stockbrokers. La Bourse, the Parisian stock exchange is only two blocks away, so this is not a touristy area, but a real working (and local eating) area, like Wall Street in New York. This restaurant is located in the second arrondissement with covered alleyways, after which the classiest of today's indoor malls were modeled. Come at night and you will have the romantic French restaurant of the movies, with food to match the ambiance.
Alain Ducasse also has his restaurant here in the 2nd called Aux Lyonnais. It serves the classic French frog's legs, chicken, beef and pork from the Lyon region (known in France for being one of the best places to eat in a country where eating is the national obsession). The food here is heavier, the peasant style of the farmer's of France. So if you like meat and potatoes, this is the French equivalent of an Midwestern style country restaurant. You will leave smiling and feeling very full.
My favorite restaurant in this area is on the Bistrot Vivienne, with it's Art Deco interior and excellent menu of all the typically French dishes from grilled Espadon (fish) to a filet de boeuf bearnaise, you can't go wrong with anything on the menu. The prices are in line with a good restaurant, but not extravagant. Lunch here is business casual, but come for dinner, dress up and spend a few hours eating, drinking, and being merrily French.
Three choices for the second arrondissement in Paris. What would I choose? I would choose to stay long enough to eat at all three:)