The original Farmer's Market at 3rd St. and Fairfax in Los Angeles is more a shopping and eating destination than a market these days. Yes, there are still vendors selling meat, poultry, vegetables, and fruits, but those vendors are outnumbered about 10 to 1 by the many places that sell hats, cards, gifts, jewelry, and food shops which sell everything from hot sauce to roasted nuts.
One of my favorite shops is the French market Mr. Marcel Pain et Vin (bread and wine). The market hosts wine tastings in their wine cellar, and the shop boasts shelves of olive oils, pastas, saffron, foie gras, and aged balsamic vinegars of the highest quality. If you love to cook, you can find what you need here if you can't find it elsewhere. With a large deli case of cheeses and prepared foods, you can skip the cooking and just take something home if you are feeling inspired but tired. Better yet, have your meal at the restaurant directly in front of the shop and have your quiche, salad, or fondue prepared for you. I love their merguez sausage and rack of lamb, but save room for their tarte tatin (apple tart), which is the best I've ever had outside of France.
If you miss New Orleans, go to the Gumbo Pot where they offer all the classics including oyster poor boys, crawfish, boiled shrimp, gumbo (mild or hot), cornbread, and wonderful freshly made beignets (kind of a puffy doughnut) to go with your chicory coffee. They offer different hot sauces to heat up your choices if they are not spicy enough. This place is as close to NOLA food as you will find in LA, so go on a humid day to get a "laissez les bon temps roulez" (let the good times roll) experience.
Brazilians love their meat, and they love it grilled in Churrascaria restaurants, just like Americans love their BBQ joints. If you crave meat, then go to Pampas Grill which offers long skewers loaded with different cuts of beef, chicken, pork, lamb, and sausage. The place is cafeteria style; you pick out your side dishes before arriving at the meat counter to choose your meat selection. Prices are based on weight, so you literally pay only for as much as you eat (or as much as your eyes say you will eat). The location in the Farmer's Market is a scaled down version of the restaurants in other parts of the city that offer a set price and serve unlimited servings carved table side, so if you like the food here, go to one of the full service Pampas Grills located all over the city.
French, Cajun, or Brazilian? Maybe a bit of each, starting with a Cajun breakfast of beignets and chicory coffee, then a Brazilian grilled meat and greens lunch, and ending with a candlelit French meal served under the stars. There are many more options to explore here, but we're off to a good start sampling three continents worth of food in one day.