How to Make It
In a food processor, pulse 1 1/4 cups flour with 1/2 teaspoon of salt. Add the butter and pulse until the mixture resembles coarse meal, with some pea-size pieces of butter still visible. Sprinkle with the ice water and pulse until the dough just starts to come together; you should still see small pieces of butter. Scrape the dough onto a work surface, gather up any crumbs and pat the dough into a disk. Wrap in plastic and refrigerate for 1 hour or for up to 3 days.
Preheat the oven to 350°. On a lightly floured work surface, roll out the dough to a 12-inch round, 1/4 inch thick. Carefully transfer to a 9-inch pie plate and trim the overhang to 3/4 inch. Fold the overhanging dough under itself and crimp decoratively. Arrange the peaches in a starburst pattern on the bottom of the pie.
In a small bowl, stir the remaining 1/3 cup of flour and 1 teaspoon of salt with both of the sugars and the cornstarch. Sprinkle evenly over the peaches. Spread the crème fraïche over the peaches and bake for 1 hour and 30 minutes, until the crust is browned and the filling is bubbling. Transfer the pie to a rack and let cool until slightly warm, at least 1 hour. Cut into wedges and serve.