Combine the raspberry preserves and 1/2 cup water in a medium saucepan, then add the raspberries and blackberries, keeping a few of each aside for topping.
Bring the preserve-berry mixture to a boil, then reduce the heat and simmer until slightly thickened, about 5–10 minutes; keep warm on low.
In a mixing bowl, whisk together the beaten eggs, half-and-half, cinnamon, nutmeg, and a pinch of salt until combined.
Heat a large skillet over medium heat and add enough butter to coat the pan.
Dip each slice of ciabatta into the egg mixture, letting excess drip off, then cook in the skillet in batches until golden brown, about 3–4 minutes per side; add more butter as needed for crisp edges.
Transfer cooked French toast to plates, drizzle with the warm preserve and berry sauce, top with reserved fresh berries, and dust with powdered sugar before serving.