Most of the brasseries, such as Balzar and Coupole mentioned earlier, are open on Sunday. Go on-line and find the Flo group website, where you can reserve on-line. If you are in the 7th, Thoumieux is similar.
L'Ardoise in the first arr. is open Sunday. It is very busy, but the food is good and the place fun. Also open Sunday is the friendly and fun Le Cave a L'Os a Moelle and its bistro L'Os a Moelle, with one of the best and best priced 6 course dinners in Paris. Good wine at both places.
Brasserie Balzar and La Coupole, both Flo Brasserie restaurants, are open on Sunday for lunch. Another one we haven't tried, but is on our list for a Sunday next Paris trip is Le Reminet, as I have heard good things about it on this board. http://tinyurl.com/337yu4