In the bowl of a stand mixer fitted with a paddle attachment (or in a large mixing bowl with an electric hand mixer), combine cake mix, pudding mix, eggs, water, oil, sour cream, and vanilla extract.
Mix on low speed for about 30 seconds to combine, then scrape down the sides of the bowl. Increase mixer speed to medium-high and beat for about 2 minutes.
Pour batter into prepared bundt pan. Bake for about 45-50 minutes, until a toothpick inserted in the center comes out clean.
Remove cake from oven and let sit for 10 minutes. Gently slide a knife around the edges of the pan to loosen the cake, then invert cake pan onto a plate.
Cool completely, then dust with powdered sugar if desired and serve.
Notes
If you can't find french vanilla cake mix, regular vanilla cake mix will work fine as well.
If you'd like a cream cheese icing to drizzle on the cake, you can beat together 4 oz softened cream cheese, 2 TBSP softened butter, and 1 cup powdered sugar. Then mix in up to 6 TBSP milk until desired consistency is reached. Drizzle over warm cake.
If you'd like a lemon glaze to brush onto the cake, whisk together 1 1/2 cups powdered sugar, 3 TBSP fresh lemon juice, and 1/4 tsp vanilla extract. Drizzle over or brush onto a warm cake and let it soak into the cake.