Remove neck and giblets from hen; reserve for another use or discard. Pull off and discard any pockets of fat. With poultry shears or kitchen scissors, split bird in half lengthwise through breastbone and backbone. Rinse halves and pat dry; set, skin up and slightly apart, on a lightly oiled rack in a foil-lined 10- by 15-inch baking pan. Arrange carrots slightly apart alongside.
Roast in 425° regular or convection oven until hen is lightly browned, 20 to 25 minutes.
Meanwhile, in a small bowl, mix maple syrup and mustard. Rinse and string snap peas if using fresh.
Remove pan from oven and brush hen halves and carrots with mustard mixture, turning as needed to coat all sides. Set halves skin up on rack and continue roasting with carrots until meat at thigh bone is no longer pink (cut to test), 10 to 14 minutes longer.
About 8 minutes before hen is done, in a 1- to 1 1/2-quart pan over high heat, bring broth, corn, snap peas, and peppercorns to a boil. Stir in couscous. Cover pan and remove from heat; let stand until broth is absorbed and couscous is tender to bite, about 5 minutes.
Mound couscous equally on plates. Set a hen half on each mound and arrange carrots alongside couscous. Add salt and pepper to taste.