There is a huge Auchan supermarket at the Val d'Europe shopping centre in Marne La Vallee (1 stop on train from Disney). Some of the food in the parks is actually quite good and reasonable priced, for example the breakfast deals in the backlot cafe at disney studios. It is the same as anywhere else - there is good food and bad food - take a sneaky look at other peoples plates as you walk past to see if you like the look of it. Across the resort there is a reasonable variety. Look for set meals in the nicer sit down restaurants as these are more reasonably priced.
Technically you are not allowed to take food into the parks, however, remember that you can leave the parks and come back - just keep your ticket and get your hands stamped at the gate. This means that you can go back to your hotel room at get something to eat and a rest - it can be very tiring for everyone, not just the little ones. Again, you could also jump on the train to Val d'Europe for lunch where there arre some excellent restaurants.
As long as your child is not scared of the characters - they can be a little daunting for little ones - I would recomend a character dinner for some great photos!