This paper investigates the optimal resource allocation in free space optical (FSO) fronthaul networks. The optimal allocation maximizes an average weighted sum-capacity subject to power limitation and data congestion constraints. Both adaptive power assignment and node selection are considered based on the instantaneous channel state information (CSI) of the links. By parameterizing the resource allocation policy, we formulate the problem as an unsupervised statistical learning problem. We consider the graph neural network (GNN) for the policy parameterization to exploit the FSO network structure with small-scale training parameters. The GNN is shown to retain the permutation equivariance that matches with the permutation equivariance of resource allocation policy in networks. The primal-dual learning algorithm is developed to train the GNN in a model-free manner, where the knowledge of system models is not required. Numerical simulations present the strong performance of the GNN relative to a baseline policy with equal power assignment and random node selection.