Although you can get organic produce at shops like Naturalia or Les Nouveaux Robinson, It is best to buy them directly from the local farmers and markets. There are tons of markets around Paris, however, there are 2 that I am particular fond off because of the quality of the products. They are:
Le marché d’Aligre. Great varieties of cheeses, meat, organic fruits and veggies as well as antique books, accessories and furnitures. Hours of operations: Tuesdays&Fridays 7:30 am-1:30 pm, Saturdays&Sundays from 7:30 am-2pm.
Address: Place Aligre, 75012 Paris. Directions: Line 8. Get off at Metro Ledru Rollin
Le marché Port-Royal 75005 Paris( see photo above). Great if you are into organic produce as well. Hours of operations: Tuesdays & Thursdays 7 am-2pm and Saturdays from 7am-3pm.
Address: Boulevard de Port-Royal. Directions: Line RER B get off at Port-Royal.
Disclaimer: All photos are mine unless specified.