To make the French toast: Preheat oven to 350 degrees F.
Whisk together eggs, milk, sugar, and salt until blended. Pour into a large baking pan and soak bread slices in 1 layer, turning once, 8 minutes.
Prepare berry sauce while bread is soaking. Puree 1 1/2 cups berries with sugar and lemon juice in a blender. If you want to eliminate seeds, force puree through a very fine sieve into a bowl. Transfer to a serving bowl and fold in remaining berries.
Heat 1 1/2 tablespoons butter in a 12-inch heavy skillet or griddle over moderately high heat until foam subsides. Transfer 4 soaked bread slices to skillet with a slotted spatula and cook until golden brown, about 1 minute on each side. Cook remaining bread in 2 batches, adding more butter as needed. Transfer slices as cooked to a large shallow baking pan (using a clean spatula) and, when all are browned, bake in middle of oven until hot, about 5 minutes.
Dust French toast with confectioner's sugar and serve with berry sauce.