1. Preheat oven to 375°. Whisk 1 1/2 cups flour, 3 Tbsp. sugar, baking powder, and salt in a large bowl. Add butter; using your fingertips, incorporate until only pea-size lumps remain. Gently mix in crème fraîche. Knead in bowl until a biscuit-like dough forms, 5–7 turns (overmixing will make dough tough).
2. Combine remaining 1 cup sugar, remaining 3 Tbsp. flour, berries, juice, and zest in a large bowl. Toss to coat. Pour into an 8x8x2" glass baking dish or divide among six 6-oz. ramekins. Tear biscuit topping into quarter-size crumbles; scatter over berries.
3. Bake cobbler until juices are thick and bubbling and topping is cooked through and deep golden brown, 20–25 minutes for ramekins or 45–50 minutes for baking dish. Let cool for at least 1 hour.