Heat oven to 350 degrees and coat an oval baking dish with cooking spray. An 8x8 baking dish will work too.
Place peaches into a pot of boiling water until the skins begin to peel. Remove from heat and drain. Peel off peach skins with a knife and slice to your preferred size.
In a large bowl, combine sliced peaches, blackberries, sugar and flour until well combined. Pour into prepared baking dish and set aside.
Combine flour, oats, sugars, cinnamon and salt until well blended. Cut butter into small pieces, add flour mixture and use a pastry cutter or your hands to incorporate the butter to create a crumb mixture.
Spoon the crumb mixture evenly over the filling.
Bake in the oven for 40 - 50 minutes, until topping starts to brown and fruit filling is starting to bubble on the sides.
Let cool for 10 minutes and serve with dairy-free whipped cream or ice cream.