Line a baking sheet with parchment paper and turn on oven to 400°.
Place peaches and blackberries in small, separate bowls. Add half of lemon juice, cane sugar and cornstarch to peach slices and toss together. Add other half of lemon juice, cane sugar and cornstarch to blackberries and toss together. Set them aside.
On a floured surface, roll out puff pastry and cut pastry into eight squares (or rectangles). Transfer eight puff pastry squares onto the baking sheet.
Layer 3-4 peaches and arrange 3 blackberries over each puff pastry square.
Brush around the pastry edges with egg wash and bake in the oven for 18-20 minutes or until puff pastry turns golden brown.
Cool tarts in the cooling rack for 5-10 minutes before serving. Serve with powdered sugar if desired.