Preheat the oven to 170 degrees.
In a medium bowl, stir together the eggs, milk, maple syrup, vanilla extract, and cinnamon.
In a medium skillet, melt the butter over medium heat. Turn the heat down to medium low.
Dip two pieces of bread (one at a time) into the egg mixture. Let them soak for several seconds so they gets saturated.
Carefully transfer the bread to the skillet. Cook the bread over medium heat on one side for about two minutes, then flip both pieces.
Place half a banana, thinly sliced, on top of one piece of bread. Place the other slice on top, cooked side down (touching the bananas). Let the sandwich cook for about 2 minutes, until the bottom is well browned. Flip the stack and cook on the other side for 2 minutes. Remove the French toast from the pan and place it in a covered dish in the oven to keep it warm.
Repeat with the remaining slices of bread. As each sandwich is cooked, place it in the covered dish in the warm oven so everyone can eat together.
Serve warm with a little maple syrup or berry sauce.