Preheat oven to 425 degrees. On a lightly floured surface and using a floured rolling pin, roll puff pastry into a 10 1/2-inch square. Brush off excess flour. Using a plate as a guide, cut out a 10-inch round. Transfer pastry round to a parchment-lined baking sheet, and refrigerate until firm, about 30 minutes.
Meanwhile, coat bottom and sides of a 10-inch skillet with the 4 tablespoons butter. Sprinkle sugar evenly over bottom. Arrange apple slices closely together in concentric circles in skillet, with rounded sides down. Place over medium-high heat, and cook, without stirring, until juices are deep golden and bubbling, 18 to 20 minutes.
Line oven rack with foil to catch any juices, and place skillet on foil. Bake for 20 minutes (apples will settle slightly). Remove from oven, and place pastry round over apples. Bake until pastry is dark golden brown, 23 to 28 minutes. Let cool in skillet on a wire rack for 10 minutes before serving.
Invert tart onto a serving dish. Gently remove any apples that stick to skillet, and place on tart. Serve warm, with creme fraiche.