In a small skillet, toast the saffron over medium heat for about 1 minute; transfer to a small bowl and let cool. Crumble the saffron threads and stir in 1 1/2 teaspoons salt, 1/8 teaspoon pepper and the ginger. Rub the chicken all over with the saffron-ginger mixture; let sit.
Preheat the oven to 450 degrees . In a saucepan, bring 1 cup water to a boil; remove from the heat. Stir in the couscous, cover and let stand until the water is absorbed, 10 minutes. Fluff with a fork, then stir in 2 tablespoons butter, the almonds, sugar and cinnamon; season with salt and pepper. Let cool.
Meanwhile, in a large, ovenproof skillet, heat 2 tablespoons butter over medium heat. Add the onions and cook, stirring occasionally, until softened, about 10 minutes. Add the chicken broth; season with salt.
Measure out 2 cups of the couscous mixture; reserve the remainder. Stuff the chicken with the 2 cups mixture and tie the drumsticks together. Place the chicken on the onion mixture in the skillet, transfer to the oven and roast for 30 minutes. Lower the heat to 350 degrees and roast until the chicken is cooked through, 35 to 40 minutes. Transfer the chicken to a cutting board. Remove the stuffing and toss with the reserved couscous mixture.
Transfer the onion mixture to a food processor and puree. In a small skillet, heat the remaining 1 tablespoon butter over medium-high heat. Add the peach slices and cook, turning once, until browned, about 3 minutes. Serve the chicken with the peach slices, couscous and onion gravy.