Combine the caramel sauce, thyme sprigs and 2 tablespoons water in a small microwave-safe bowl and microwave until hot, about 1 minute. Cover and keep warm.
Cut the baguette into 4 long, angled slices. Divide half of the cheese among 2 bread slices; sprinkle with half of the chives. Top with the apple slices and the remaining cheese, chives and 2 bread slices.
Melt the butter in a large skillet over medium heat. Add the sandwiches and cook, pressing occasionally with a spatula, until the bread is toasted and the cheese melts, about 4 minutes per side, adding more butter to the pan if needed.
Remove the thyme from the caramel sauce and sprinkle with sea salt. Serve with the sandwiches for dipping.