In a large skillet, over medium-low heat, melt 2 tablespoons of the butter until it foams. Add the brown sugar and stir for 30 seconds. Add the peaches, raise heat to medium-high, and cook, stirring frequently, for 3 minutes. Stir in 2 tablespoons of the cream and simmer for 2 minutes. Transfer to a bowl.
Heat oven to 200° F. Place 4 slices of the bread on a cutting board. Divide the peach mixture evenly among the slices, leaving a 1/2-inch border on all sides. Top with another slice of bread and press gently. In a shallow bowl, beat the eggs and cinnamon. Working in batches, soak the sandwiches in the egg mixture for 2 minutes per side. Melt 1 tablespoon of the butter in a large skillet over medium heat. Fry 2 sandwiches until golden brown, 3 to 4 minutes per side. Transfer to a baking sheet and place in oven to keep warm. Repeat with the remaining butter and sandwiches. Beat the remaining cream until soft peaks form. Halve each sandwich on the diagonal, sprinkle with the confectioners' sugar, and serve with the whipped cream.
Tip: If you're using day-old bread to make the French toast, trim the crusts, which may have become tough.