Eating inside the palace grounds is possible but expensive and mediocre — the cafeteria near the Orangerie and La Flottille on the Grand Canal are both overpriced for what they are. For a proper meal, walk the 10 minutes into town.
The Place du Marché Notre-Dame is your best option. The square around the covered market is lined with brasseries and cafes, many with outside tables, and the cooking is straightforward French without pretension: steak frites, onion soup, roast chicken. The market itself sells excellent cheese and charcuterie if you want to eat informally.