We present a 3-D shear wave velocity model of the Mauleon and Arzacq basins from the surface down to 10~km depth. This model is obtained by inverting phase velocity maps for periods from 2 to 9~s measured on coherent surface wavefronts extracted from ambient seismic noise by matched filtering. This new model, which is found in good agreement with local earthquake tomography, reveals the architecture of the Mauleon and Arzacq basins which were poorly imaged by conventional reflection seismic data. Combining these new tomographic images with surface and subsurface geological information allows us to trace major orogenic structures from the basement to the surface. In the basin, the models are successfully imaging first-order folds and thrusts at kilometric scale. The velocity structure within the basement and its geometrical relationship with the base of inverted rift basins supports a progressive northward exhumation of deep crustal and mantle rocks in the hanging wall of north-vergent Pyrenean thrusts. Our tomographic models image in 3-D orogen-perpendicular structures responsible for crustal segmentation as the Saison and Barlanes transfer zones. We propose that these steep structures consist in tear faults that accommodate the deepening of the Mauleon basin basement from west to east. To the west, this basement made of former hyper-extended rift domains (including mantle rocks) is anomalously sampled within the hanging-wall of north-directed orogenic thrusts, explaining its shallow attitude and its best preservation in comparison to the eastern segment of the study area. Eastward, the vertical shift of the basement makes that the former Mauleon basin hyper-extended rift basement remained in a footwall situation in respect of orogenic thrust and was underthrust. The comparison of the tomographic models obtained with surface wave tomography and local earthquake tomography shows that each approach has its own advantages and shortcomings but also that they are very complementary in nature, which would suggest to combine them in joint inversions to further improve passive imaging of the shallow crust and sedimentary basins.