Preheat oven to 400 degrees F.
Peel and slice the peaches and put in a deep bowl. Add the sugar, flour, and salt and mix. Save the Demerara sugar for later.
Place the pie crust flat along the bottom of a nine-inch pie pan with the edges sticking up.
Pour in the peach mixture and fold the sides of the crust over the peach filing, leaving an uncovered hole in the center of the pie.
Bake for 20 minutes, then sprinkle the top with the Demerara sugar. Return to the oven and bake for an additional 20-25 minutes.
Remove from the oven and let cool.