Make the Topping: With an electric mixer, combine the flour, sugars, cinnamon, and salt on low speed until well combined, about 45 seconds. Add the butter and continue to mix on low speed until the mixture resembles wet sand and no large butter pieces remain, about 2½ minutes. Transfer to a small bowl and set aside.
Make the Cake: Adjust oven rack to lower-middle position and preheat oven to 350 degrees F. Grease a round 9-inch cake pan, line the bottom of the pan with parchment, grease the parchment, then flour the inside of the pan.
In a small bowl, whisk together the flour and baking powder; set aside. Using an electric mixer, cream together the butter, sugar and salt at medium-high speed until light and fluffy, about 3 minutes, scraping down the sides of the bowl as needed. Add the vanilla and beat until combined, about 30 seconds. Reduce the mixer speed to medium, then add eggs one at a time; beat for 5 to 10 seconds, then scrape down bowl and continue to beat until fully incorporated (mixture will appear broken). Reduce the mixer speed to low, then gradually add the flour mixture and beat until the flour is almost fully incorporated, about 20 seconds. Use a rubber spatula to finish mixing until no flour pockets remain (the batter will be very heavy and thick). Using the rubber spatula, gently fold blueberries and peaches into the batter until evenly distributed.
Transfer batter to prepared pan; use an offset spatula to gently spread the batter evenly to the pan edges and smooth the surface. Squeeze a handful of the streusel in your hand to form a large cohesive clump; break up the clump with your fingers and sprinkle evenly over batter. Repeat with remaining streusel.
Bake until the top is deep golden brown and a thin knife inserted into center of the cake comes out clean, about 55 minutes. Place on a wire rack for 20 minutes (the cake will fall slightly as it cools).
Run a thin knife around the sides of cake. Invert the cake, then peel off the parchment from the bottom of the cake and discard. Turn the cake right-side-up onto a cooling rack or serving dish. Allow to cool for at least 1 hour. Serve warm or at room temperature. Leftovers can be stored at room temperature, in an airtight container or wrapped in plastic wrap, for up to 2 days.