We just returned from a week in the 4th with our two children (5 and 8). We managed to have some amazing restaurant meals for lunch--where the children had steak hache and pomme frites while we lingered though our courses. I highly recommend Cafe des Musees (technically in the 3rd) for lunch. The lunch menu of a slightly warm lentil soup with greens was followed by a course of duck with mashed potatoes, turnips and an amazing wine sauce was simply perfect on a winter day. The cheese plate was good, albeit the cheese choices a little more pedestrian than we we had hoped (including a standard goat and camembert). The place is noisy, crowded and busy but we never felt rushed and the service was always good--just never expect to have a quick lunch. This is the one place in Paris where we got a reasonably-priced quality meal (18 Euros for the menu) like I've come to expect from our visits to Provence (Cafe de la Poste in Goult being my ultimate favorite). The other bonus is that it's open on Saturday and Sunday!
For dinners, we cooked at home and would recommend the few blocks on rue de Rambuteau between rue Beaubourg and rue des Archives. The pastries at Le Pain de Sucre (14 rue Rambuteau) are mouth watering works of art--meant for a nice splurge. Their whole wheat baguettes are fantastic if you're lucky enough to have them as your local boulangerie.
Cheeses at Fromages...ou desserts (13 rue Rambuteau) were amazingly good and the selection wonderful--although the shopkeeper was not very open and engaging. The shopkeeper at Nicolas on the other side of the street was unpretentious and gave excellent wine recommendations in a broad range of price points--providing us with a marvelous bottle of wine for 5 Euros. Perfect for a picnic or a dinner at home.