Check out this website for a listing of all the Sunday markets in Paris. The first listing for the 6th is the one where I live - it is organic and fantastic! Fresh hot galettes are a specialty. Also, the fresh made thick traditional French hot chocolate - mmm!!
In the 13th district is a HUGE outdoor market, where you can find everything! There you can find all the different countires represented, with Portuguese fried fish balls, Polish sausages, and Turkish flat bread sandwiches, among many other delicacies. Certain weekends, there is also an outdoor flea market in combination with the food market.