Preheat the oven to 350F. Grease the interiors of two 9-inch pans. Line the bottoms with parchment paper.
For the Cake:
In a medium bowl, combine the flour, baking soda, salt and baking powder. Combine evenly by stirring gently with a whisk.
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 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 inserted in the middle comes out clean, about 30 minutes.
Cool the cakes in their pans for 10 minutes. Unmold the cakes by running a small knife around the inside edges of the pans. Invert the cakes onto a wire rack. 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.
For 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 creme fraiche, cream, and remaining 2 tablespoons sugar until stiff enough to hold its shape but is still smooth.
To Assemble the Cake:
Place a cake layer on a serving platter. Spread one quarter of the creme fraiche filling on top of the cake. Top with one quarter of the blueberry sauce and then one quarter of the raspberries. Place a second cake layer on top and spread creme fraiche, blueberry sauce, and raspberries 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 an 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 up to 2 days in advance; wrap well in plastic wrap and store at room temperature. The blueberries can be cooked 2 days in advance and kept refrigerated. The creme fraiche and cream should be whipped just before assembling. The cake should be assembled the day it is going to be eaten.