For the past few years, the increase in high bandwidth requiring services forced telecommunication operators like France Telecom - Orange to engage the deployment of optical networks, the Fiber To The Home Gigabit Passive Optical Network (FTTH GPON) technology, leading to new design problems. Such problems have already been studied. However, to the best of our knowledge, without taking into account the future demand uncertainty. In this paper, we propose a model for a two-stage robust optimization FTTH network design problem tackling the demand uncertainty. We propose an exact algorithm, based on column and constraint generation algorithms, and we show some preliminary results.