Infuse fruit in rum: Mix fruit and rum, let it sit overnight in the refrigerator (or 8 hours). When it's time to make the pudding separate the fruit from the rum, discard the rum, and set fruits aside to use later in the preparation.
Prepare pudding mixture: Crack eggs into a bowl. Add sugar and whisk until it is well mixed and a slightly lighter color. Pour in milk followed by the cinnamon and mix well. Add the bread and stir until all of the bread has soaked some of the liquid. Cover and let it rest in the refrigerator for an hour.
Prepare baking pan: Mix water and sugar for the caramel in a small saucepan. Heat over medium-high heat until it turns into a golden color. Remove from the heat and immediately pour it into a baking pan (see notes). Make sure to use a holder to grab the pan, as it will be very hot. Coat the pan with the caramel, working quickly before the caramel sets. Once the caramel has hardened, cover the bottom of the pan with the fruit.
Making the pudding: Spoon the pudding mixture into the baking pan, making sure not to disturb the caramel or fruits. Cover the pan very tightly with the pudding with aluminum foil.
Cook and serve: Bake in a bain-marie (hot water bath) for an hour in an oven preheated to 300 ºF [150 C]. Remove from the oven and separate the edge from the pan with a toothpick. Let the pudding cool to room temperature and place it on a serving plate. Serve at room temperature.