Whisk together the mascarpone and maple syrup in a small bowl; set aside.

Whisk together eggs, egg yolks, sugar, salt, and cinnamon in a large bowl until combined. Whisk in the half-and-half and vanilla and whisk until smooth. Transfer the custard to a large baking dish. Add 4 slices of the bread and let soak on one side for 4 minutes. Turn the bread over and let soak 4 minutes more.

Three minutes before the bread is done soaking, combine 2 tablespoons of the oil and 2 tablespoons of the butter in a large non-stick cast iron skillet and heat over medium heat until the butter has melted and the mixture begins to shimmer. Check to make sure that the bread is completely soaked through with the custard, then remove it from the custard with a fish spatula and transfer it to the pan, leaving room between each slice. Cook until the bottoms are golden brown and crispy on the second side, about 3 minutes more. Transfer to a wire rack set over a baking sheet and keep warm in a 250 degree oven. Repeat to soak and cook the remaining slices of bread.

Serve the french toast topped with the maple mascarpone and compote.

Combine the peaches and sugar in a large bowl and let sit, stirring a few times, until the juices release, at least 15 minutes. Transfer to a large saute pan and cook over high heat until soft about 5 minutes. Add the peach liqueur and cook for 1 minute longer, until the liquid has reduced and all the alcohol has cooked off.

Remove from the heat and stir in the raspberries, lemon zest, and lemon juice. Let sit until the raspberries begin to soften, about 5 minutes. Transfer to a bowl and serve warm or at room temperature.