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 creme fraiche. Knead in bowl until a biscuit-like dough forms, 5-7 turns (overmixing will make the dough tough).
Combine remaining 1 cup sugar, remaining 3 tablespoons flour, berries, juice and zest in a large bowl. Toss to coat.
Pour into a 8 x 8 x 2 inch baking dish or into six 6-oz ramekins. Tear biscuit topping into quarter-size crumbles. Scatter over the berries.
Bake cobbler until the juices are thick and bubbling and topping is cooked through and deep golden brown, 20-25 minutes for ramekins ro 45-50 minutes for the baking dish. Let cool for at least one hour.