Preheat the oven to 350 degrees . Butter a 9-by-2-inch round cake pan. In a small, heavy saucepan, bring the sugar, 2 tablespoons maple syrup and 1/2 cup water to a boil over medium-high heat, without stirring, and cook for 5 minutes. Boil until the caramel is a light golden color or a candy thermometer registers 240 degrees , 5 to 8 minutes longer. Working quickly and carefully, remove the thermometer and pour the maple caramel into the prepared cake pan. Set aside.
In a large bowl or baking dish, whisk the milk, eggs and the remaining 1/4 cup maple syrup. Soak the croissant halves in the custard until moistened, then layer the croissants on top of the maple caramel in the prepared cake pan, pressing down gently to flatten. Pour any remaining custard over the croissants and let the bread soak and soften, pressing down occasionally to flatten the croissants.
Set the cake pan in a large roasting pan and carefully pour enough hot water into the roasting pan to reach halfway up the sides of the cake pan. Bake until the croissants are golden and the custard is set (a toothpick inserted in the center of the French toast should come out clean), about 45 minutes. Remove the French toast from the hot-water bath, cut into wedges and serve warm.