The propagation of a laser-driven shock wave in an aeronautic composite material is investigated. The material, made of three-dimensional carbon fiber lattices embedded in an epoxy matrix, is heterogeneous and anisotropic, due to the intrinsic anisotropy of the carbon fibers and to the weaving process. The shock is generated by a 10 ns laser pulse, focused on the material surface. Its ablation results in an expanding plasma, which induces a shock wave in the material with a peak compression stress of a few GPa. Starting from an optical microscopy visualization of the weaving, a differentiation between resin and fibers and a segmentation of the fibers lead to an evaluation of the material's local elastic properties below the laser spot position. The shock propagation is simulated using a nonlinear source model, combined with a time domain finite difference discretization of the equations of linear elastodynamics with Lebedev's scheme adapted to the material anisotropy. The high frequency content of the signal, the material heterogeneity and anisotropy induce a complex propagation. A measurement campaign has been performed for several samples and repeated laser illuminations. Experimental data are statistically compared to the model outputs and discussed.