Preheat the oven to 350 degrees F (175 degrees C).
Mix peaches, blackberries, 1/4 cup sugar, lemon juice, and cinnamon in a large bowl.
Pour melted butter into a 9x13-inch glass baking dish, tilting to coat the bottom and sides evenly.
Whisk flour, remaining 1 cup sugar, baking powder, and salt in another large bowl; mix in milk, stirring until just moist. Pour batter into the prepared baking dish; distribute fruit mixture evenly over batter.
Bake in the preheated oven until golden brown, about 45 minutes.