Preheat oven to 200°. Set a wire rack in a baking sheet; set aside. In a large, wide bowl or pie plate, whisk eggs to blend. Whisk in milk, granulated sugar, vanilla, cinnamon, and salt until combined. Add 2 bread slices to egg mixture and let soak, partially submerged, until bottom half of bread is saturated, about 30 seconds. Using a fork, flip bread and soak 30 seconds longer. Meanwhile, in a large skillet over medium heat, heat 1 teaspoon butter and 1 teaspoon oil just until butter starts to bubble. Add soaked bread and cook until golden brown and crisp on both sides, about 3 minutes per side. Transfer French toast to reserved rack and place in oven to stay warm. Repeat with remaining butter, oil, and bread. Divide French toast among plates. Serve with more butter and maple syrup alongside.