The daily, year-round marché at Place Richelme in Aix-en-Provence is tucked into the center of the Old Town and has been going on since the 14th century. It is just south of another large square at the Clock Tower (l'horloge) and City Hall (Hotel de Ville) -- where there is a large flower market on Tues, Thurs and Saturdays!
Walk around the market and get a sense of what all the stands have to offer. You can find fruits, veggies, bread, cheese, seafood, meat, eggs, nuts, chocolate, herbs, spices ... anything you'll need! Once you've picked a stall you want to shop at, make eye contact with the owner, ask for a Panier (basket) and let them know what you're most interested in. Most of the time I found that if they can reach it, they prefer to handle the produce themselves and will pick the freshest product for you. They don't like visitors touching all their produce - so once you touch that tomato ... put it in your panier!
You can get by without speaking French, but giving it a try will definitely please them, so use your numbers, say the french word for the product using the labels in front of the produce and say s'il vous plait (please) - you'll be amazed at how much they appreciate it!
The owners also like exact change whenever possible, so come prepared with small bills and change. If you hand them a 20€ bill for a 6.50 total, they'll still ask if you have .50 in coins.
If early, sit at a nearby cafe to watch the set-up at 9am with a coffee, toast and jam