The Earth Observation Satellite Planning (EOSP) is a difficult optimization prob-lem with considerable practical interest. A set of requested observations mustbe scheduled on an agile Earth observation satellite while respecting constraintson their visibility window, as well as maneuver constraints that impose varyingdelays between successive observations. In addition, the problem is largely over-subscribed: there are much more candidate observations than what can possiblybe achieved. Therefore, one must select the set of observations that will be per-formed while maximizing their weighted cumulative benefit, and propose a feasi-ble schedule for these observations. As previous work mostly focused on heuristicand iterative search algorithms, this paper presents a new technique for selectingand scheduling observations based on Graph Neural Networks (GNNs) and DeepReinforcement Learning (DRL). GNNs are used to extract relevant informationfrom the graphs representing instances of the EOSP, and DRL drives the searchfor optimal schedules. Our simulations show that it is able to learn on small prob-lem instances and generalize to larger real-world instances, with very competitiveperformance compared to traditional approaches.