Whisk together egg, milk, sugar, cinnamon, and 1/2 teaspoon vanilla in a large bowl.
In another bowl, stir together mascarpone, remaining 1 teaspoon vanilla, and the liqueur. Spread mascarpone mixture over 4 bread slices; top with remaining slices.
Cook maple syrup and berries in a small covered saucepan over medium-high heat on a camp stove until berries start to break down, 5 to 10 minutes. Remove from heat.
Heat a large heavy frying pan or 2 smaller ones over medium-high heat; swirl butter in pan(s). Dip sandwiches in egg mixture, then cook, turning once, until crisp and browned, 4 to 8 minutes total. Serve French toast with syrup and bacon.
PER SERVING (WITHOUT BACON) 1,215 Cal., 65% (792 Cal.) from fat; 26 g protein; 88 g fat (47 g sat.); 86 g carbo (7.5 g fiber); 705 mg sodium; 281 mg chol. V (without bacon)