An approach based on Gaussian Processes (GP) for land cover pixel-based classification with Sentinel-2 satellite image time-series (SITS) at national scale is proposed in this paper. Sparse methods combined with variational inference allow the learning of large scale GP. By using a spatio-spectro-temporal covariance function, our approach is able to use the spatial structure of the SITS in addition to the spectro-temporal structure. Experimental results conducted on 27 tiles on the south of France show that our method is effective and close to several state-of-the-art approaches (Random Forest and Deep Learning methods). Besides, the discontinuity between two spatially adjacent models independently trained is identified and quantified