Preheat the oven to 325 degrees.
Grease and flour two 8" round cake pans and set aside.
In a bowl, combine the flour, baking powder, salt and small package of dry instant french vanilla pudding. Whisk well and set aside.
In another bowl, add the french vanilla coffee creamer, milk, oil and french vanilla (or regular vanilla) extract. Whisk well and set aside.
In a large mixing bowl, add the room temperature butter and mix on medium until smooth. Add in the sugar and mix on medium and then on medium high for several minutes until light and fluffy.
Add in the eggs one at a time and mix on medium just until combined. Only mix until the egg is just incorporated. Try not to over mix. If your eggs are super cold, your batter may look a little curdled at this point, but just keep going.
Scrape down the sides of the bowl and mix again on medium, just until everything is incorporated.
Alternately add in the flour mixture and the liquid mixture. Starting and ending with the flour mixture. (Add in ⅓ of the flour mixture and mix on medium just until combined. Add in ½ the liquid mixture, mixing only until combined. Add in another ⅓ of the flour mixture, mixing only until combined. Add in the last of the liquid mixture, mixing only until combined, then the last of the flour mixture and mix until combined.)
Scrape down the sides of the bowl and mix again until well combined. You only want to mix until well combined, which is about 15 seconds. Mixing for several minutes is too long for a scratch cake.
Divide batter into the prepared pans. Batter will be quite thick so just spread it around evenly in your pans.
Bake at 325 degrees for approximately 55 - 60 minutes. The cake will be a little darker than the normal golden brown. Insert a toothpick somewhere in the middle and a few moist crumbs should stick to the toothpick.
Remove from the oven and cool in the pan on a wire rack for about 20 minutes, then turn out onto a rack and cool completely before adding buttercream.