Recent experiments show that at a critical thickness, surface forces can dominate the bulk coercing suspended Au nanofilms to globally reconstruct from the (001) to the (111) orientation. Here we perform molecular dynamics simulations demonstrating that such transformations are generic to other fcc metals. This contrasts with surface reconstruction on the bulk occurring only in 5d metals. We show that this phenomenon occurs once a small energy barrier is overcome and discuss the relation of such a barrier and the critical thickness to film surface area and boundary conditions.