Lightly grease a 9-by-13” baking dish with butter. Add the croissants and 2½ cups of the berries to the baking dish and gently toss to mix.
In a large bowl, whisk the eggs until combined. Add ⅔ cup of the granulated sugar, vanilla, lemon zest, and salt, then whisk until smooth. Stir in the milk and creme fraiche, then mix until smooth.
Pour the creme fraiche mixer over the croissants, pressing gently on the croissants with a spatula to help coat. Top with the remaining ½ cup of berries. Cover with foil and refrigerate at least 6 hours, preferably overnight.
Preheat the oven to 350°F with a rack in the center position. Transfer the covered breakfast bake to the oven and bake for 45 minutes. (The breakfast bake will be puffed and mostly set.). Discard the foil, sprinkle with the remaining 2 tablespoons of sugar, and bake uncovered until golden brown and set, about 25 minutes. (The finished breakfast bake should jiggle like a set Jell-O when it is fully cooked.) Let stand for 10 to 15 minutes.