Preheat the oven to 350 degrees. Grease a 9-inch square baking dish with butter.
In a small bowl, toss the peaches with ¼ cup flour; set aside. Whisk together the remaining flour, baking powder, cinnamon and salt in a medium bowl and set aside.
In the bowl of an electric mixer fitted with the paddle attachment, cream the butter, lemon zest and ¾ cup plus one tablespoon of sugar together until light and fluffy. Add the egg and vanilla and beat until combined.
Add flour mixture to the batter in 2 batches, alternating with the buttermilk. Gently fold in the peaches, then the raspberries. Some of the raspberries may break up but be careful not to over-mix.
Spread batter into greased baking dish and sprinkle batter with remaining tablespoon of sugar. Bake for 35 to 45 minutes, or until top is slightly golden brown and a toothpick inserted into the center comes out clean. Allow to cool for 10 to 15 minutes before serving. Enjoy!