Preheat oven to 375°F (190°C).

In a large bowl, cream together the softened butter, granulated sugar, and French vanilla instant pudding mix until smooth and well combined.

Add the vanilla extract and large eggs to the creamed mixture. Beat at low speed until fully incorporated.

In a separate bowl, sift together the all-purpose flour and baking soda.

Gradually add the dry ingredients (flour and baking soda mixture) to the wet ingredients (creamed mixture). Mix until just combined, being careful not to overmix.

Stir in the chocolate chips until they are evenly distributed throughout the cookie dough.

Drop rounded tablespoons of cookie dough onto a greased cookie sheet, spacing them evenly apart.

Bake in the preheated oven for 8 to 10 minutes, or until the edges are golden brown and the centers are set.

Remove the cookies from the oven and allow them to cool fully on a wire rack before serving. This helps them to firm up and develop their texture.