Preheat the oven to 350 degrees. Grease the bottom and side of two 9-inch cake pans. Line the bottoms with parchment paper.
To make the cake:
In a medium bowl, sift together the flour, baking soda, salt and baking powder. Beat the butter with the sugar until light, 1 minute on medium-high speed with a stand mixer or 3 minutes with a handheld mixer. On medium speed, add the eggs, one at a time, beating for 30 seconds with a stand mixer or 1 minute with a handheld mixer after each addition. Periodically scrape down the sides of the bowl.
Stir together the buttermilk and the vanilla. On low speed, add half of the buttermilk. Mix until incorporated and then scrape down the sides of the bowl. Add half of the dry ingredients. Mix until well combined and scrape down the sides of the bowl. Add the remaining buttermilk and the dry ingredients in the same manner. Stir in the poppy seeds.
Divide the batter between the two pans. Evenly spread it in the pans. Bake the cakes on the middle oven rack until a skewer (or toothpick) inserted in the middle comes out clean. (Baking time: about 15-20 minutes) Cool the cakes in their pans for 10 minutes. Remove the cakes from the molds by running a small knife around the inside edges of the pans. Place a plate or wire rack on top or each cake and invert the cake and plate. Remove the pans and let the cakes cool completely. Carefully peel off the parchment paper.
Using a serrated knife, cut each cake in half horizontally, making a total of 4 layers.
To make the filling:
Cook the blueberries and ¼ cup of the sugar in a small saucepan over medium-low heat, stirring often, until the sugar has dissolved and the berries have popped open and become juicy, about 5 minutes. Let cool to room temperature.
Whip together the crème fraiche, cream, and remaining 2 tbsp. sugar until stiff enough to hold its shape but still smooth.
To assemble the cake:
Place a cake layer on a serving platter. Spread one quarter of the crème fraiche filling on top of the cake. Top with one quarter of the blueberry sauce and then one quarter of the boysenberries. Place a second layer on top and spread crème fraiche, blueberry sauce and boysenberries on top as you did with the first cake layer. Repeat with the third and fourth layers, ending with berries on the top of the cake.
If not serving within 1 hour, refrigerate the cake. Once removed from the refrigerator, let it sit at room temperature for 15 minutes before serving, for optimal flavor.
The cake layers can be made two days in advance; wrap well in plastic wrap and store at room temperature. The blueberries can be cooked two days in advance and kept refrigerated. The crème fraiche and cream should be whipped just before assembling. The cake should be assembled the day it is going to be eaten