Combine yeast with warm water and sugar in a large mixing bowl. Let stand for 5 minutes or until yeast is activated and mixture becomes foamy.
Combine flour with salt. Add flour mixture to yeast mixture along with 2 tablespoons olive oil. Mix until dough forms. Knead dough until smooth and elastic about 7-8 minutes. Add 1 tablespoon olive oil to a clean bowl and transfer dough to bowl, turning to coat with oil. Wrap with plastic wrap and let rise for 1 hour in a warm place or until doubled in size.
Divide dough into 8 equal pieces. Spread 2 tablespoons olive oil on baking sheet and place dough on top. Loosely cover with plastic wrap and let rise in a warm place for another 30 minutes.
Preheat oven to 425 degrees F.
Dimple tops of focaccia using your fingers. Top with enough berries to cover the top, gently pressing down on the fruit. Sprinkle 2 teaspoons coarse sugar per bread and ¼ teaspoon chopped rosemary. Drizzle the remaining 2 tablespoons of oil on top.
Bake fruit focaccia for 15-20 minutes, rotating the sheet halfway. Remove and cool slightly. Sprinkle more sugar on top and serve warm or at room temperature.