Copper beeches (Fagus sylvatica Purpurea) are simply reddish varieties of the European or common beech (Fagus sylvatica).
These trees grow happily and abundantly in many European forests, for example right where I live, in the Black Forest in Germany. In a few decades the spindly saplings can grow into large, majestic trees - without any pruning.
So no, there is no need to prune if you plan to let nature take its course.
Should you have specific plans as far as future shape is concerned, you may prune if required. My gut feeling, however, would be to simply let it grow for a few more years before taking any action (if you intend to cut).