Melt butter in a saucepan over medium heat. Stir maple sugar, ginger, cinnamon, and nutmeg into the melted butter. Add peaches and stir to coat. Cook the peaches at a simmer until soft and the juices begin to thicken, about 20 minutes.
Gently fold blackberries into the peach mixture; cook until the berries soften, about 5 minutes more.