Place a large skillet over medium-high heat. Add the bacon and cook for about 6 minutes, until golden and crispy on both sides. Drain on paper towels.
Preheat a Panini press. Place four slices of bread on a clean work surface and layer the mozzarella cheese, peaches, bacon, and spinach over the bread. Place the remaining bread slices on top. Grill the sandwiches for about 5 minutes, until the bread is toasted and the cheese is melted. Transfer the sandwiches to a cutting board. Cut each sandwich in half and serve.