Place bread on baking sheet and let stand: Spread bread slices on a baking sheet; let stand at least a few hours and up to overnight.
Melt butter in skillet and add sugar, salt, and lemon juice: Melt butter in a large ovenproof, nonreactive skillet (like an 11-to-12-inch enameled cast iron) over medium heat. Add 1 cup brown sugar, ¼ teaspoon salt, and lemon juice. Cook, stirring, until sugar dissolves, then bring to a boil; cook 1 minute.
Add apples and cook: Add apples and cook, turning occasionally, until they begin to soften and brown a bit and liquid thickens, about 12 minutes. Let cool 30 minutes.
Whisk eggs, milk, remaining sugar, and vanilla: In a wide, shallow dish, whisk together eggs, milk, remaining 2 tablespoons brown sugar, vanilla, and ¼ teaspoon salt.
Dip bread and arrange over apples: Dip bread in mixture, turning to coat. Arrange atop apples, shingling in concentric circles. Pour remaining mixture on top. Cover; refrigerate at least 2 hours and up to 24.
Preheat oven and bake: Preheat oven to 350°F. Sprinkle French toast with cinnamon and bake, uncovered, until set and golden on top, 35 to 45 minutes.
Cool for 15 minutes, then dust with confectioners' sugar and serve: Let stand 15 minutes. Dust with confectioners' sugar; serve with yogurt, pecans, and fruit.
