Preheat oven to 375°. Unroll pie crust into a 9-in. pie plate; flute edge. In a large bowl, combine peaches, strawberries and lemon juice. In a small bowl, mix sugar, cornstarch and basil. Add to fruit and toss gently to coat. Transfer to crust.
In a small bowl, mix flour and brown sugar; cut in butter until crumbly. Sprinkle over filling. Place pie on a foil-lined baking pan.
Bake on a lower oven rack until topping is golden brown and filling is bubbly, 45-55 minutes. Cool on a wire rack.