The youthful Jardin du Roi is a surprisingly authentic French cafe, bar and restaurant in the heart of Chappaqua. One has to love the sheer optimism of a place that remains open for breakfast, lunch and dinner seven days a week from 8 in the morning to midnight in a town where the seriously driven population folds early to be primed for work and school the next day. Maybe its just that people in Chappaqua burn more calories than the rest of us, but in its third year, this little boîte is making a nice go of it. Le Jardin du Roi does French bistro pretty much by the numbers, but the numbers add up nicely. The decor is shabby-chic Parisian: a velvet swag here, a ceramic rooster there. The very minimal art includes a stark black and white photo of the Eiffel Tower and vintage French posters in sizes too small to have the desired effect. But the food is both artful and robust, the service engaging and attentive.