Place raspberries, blackberries, and strawberries in a bowl. Add lemon zest, lemon juice, and 1/4 cup sugar. Stir until sugar is mixed with fruit and juices begin to form. Cover and refrigerate until chilled, about 1 hour.
Place heavy cream and creme fraiche in a cold bowl. Add 1 tablespoon sugar and vanilla extract. Whisk until mixture has soft peaks and sharp lines, 5 to 8 minutes.
Place some cookie crumbs in the bottom of each serving dish. Spoon in some of the fruit and a layer of whipped cream. Repeat layers, ending with a sprinkle of cookie crumbs.