Rillettes, a kind of boiled pork pate, is the culinary specialty of Le Mans. It actually tastes much better than its description. You can buy some rillettes in almost every meat shop in town, and it makes for the perfect sandwich pasted on some fresh baguette.
A very good variety of restaurants is found in the town center and especially in or around the old city. For 50 Euros and a very good sample of French cuisine, give a try to Le Grenier A Sel, 26 Place de l'Eperon, La Ciboulette, 14 Rue de la vielle porte, or Le Nez Rouge, 107 Grande rue, all of them close or inside the old city. Le Baobab, on the same street as La Ciboulette, offers some African cuisine at the very heart of the old city.
The area closer to Place de la Republique, popular with young people on weekends, offers cheaper eats, with several kebab shops that would fill you for 10 euros or less.