This paper introduces RoCNet++, a point cloud registration method with two main contributions, one concerning the design of a robust descriptor and another concerning the estimation of the rigid transformation. First, to robustly capture the local geometric properties of the surface, i.e., each point is characterized by all the triangles formed by itself and its nearest neighbours in the 3D point cloud. The idea is to assist the learning of the descriptor by introducing a priori information about interesting geometric properties such as the invariance of triangle angles under rigid transformations. This local triangle-based descriptor is integrated into the recently developed RoCNet architecture for estimating the correspondences between source and target point clouds. We then introduce the Farthest Sampling-guided Registration (FSR), which relies on successive farthest point samplings to estimate the global rigid transformation between 3D point clouds. The new proposed architecture RoCNet++ has been evaluated in different configurations: clean, noisy and partial data on both synthetic and real databases such as ModelNet40, KITTI, and 3DMatch. RoCNet++ shows improved performances on these benchmark datasets in favourable and unfavourable conditions. Furthermore, both the local triangle-based descriptor and the Farthest Sampling-guided Registration (FSR) can be used in other registration algorithms.