In a large bowl, whisk together the instant French vanilla pudding mix and whole milk for 2 minutes (according to package directions) until the pudding has started to thicken. Set aside.
In a separate large mixing bowl, using a hand mixer on medium speed, beat the cream cheese for 1 to 2 minutes or until smooth and fluffy. Add the granulated sugar and vanilla extract and continue to beat for another minute.
Add the French vanilla pudding to the bowl with the cream cheese mixture. Fold together to fully incorporate both the cream cheese and pudding to create a smooth filling.
Cover the bottom of a 9x13-inch baking dish with a single layer of graham crackers. This will use one of the three individual packages inside the box of graham crackers. You may need to break some of the larger crackers to fit in the pan.
Using half of the cream cheese and pudding mixture, spread an even layer over the top of the first layer of graham crackers.
Next, distribute 1 cup of the sliced strawberries and ½ cup of blueberries evenly over the first layer of filling.
Place another single layer of graham crackers over the layer of berries, followed by the remaining half of the French vanilla cream cheese filling, and spread it out evenly over top of the graham crackers.
Top this layer with the remaining 1 cup of sliced strawberries and another ½ cup of blueberries.
Using the remaining graham crackers, cover the berries with a final layer.
Top the final graham cracker layer with the thawed whipped topping spread into an even layer.
Decorate the top of the berry icebox cake with 1 cup of halved strawberries and the remaining ½ cup of blueberries.
Refrigerate for 6 hours or up to overnight, before slicing and serving.