Preheat the oven to 350 degrees F.
For the caramelized peaches:
Combine the peaches, granulated sugar, muscovado sugar and peach eau de vie in a large bowl. In a heated pan, add the butter and vanilla extract. Toss in the peaches and cook just to heat through, about 5 minutes. Toss again with the mint. Set aside and keep warm.
For the pain perdue:
Whisk together the eggs and sugar in a large baking dish until combined. Add the cinnamon, salt, nutmeg, milk, cream and vanilla extract and whisk until smooth. Add the bread, in batches and let soak on each side for 1 to 2 minutes until soaked through. While the bread is soaking, heat 2 tablespoons of the butter and 2 tablespoons of the oil on a large griddle over medium-high heat until butter is melted and oil begins to shimmer.
Spread the feuilletine crushed wafers in a large baking dish and dip the bread on each side in the mixture, pressing gently to adhere. Place the bread on the hot griddle and cook each side until golden brown.
Transfer to a baking sheet and bake in the oven to completely heat through, about 5 minutes. Serve 2 pieces per person, topped with a dollop of the vanilla butter and spoonfuls of the caramelized peaches. Top with maple syrup and mint and serve.
Vanilla Bean Butter:
Stir together the butter, vanilla bean seeds, sugar, and salt in a small bowl until combined.