This article proposes a fast texture-based supervised classification framework for fully polarimetric synthetic aperture radar (PolSAR) images with very high spatial resolution (VHR). With the development of recent polarimetric radar remote sensing technologies, the acquired images contain not only rich polarimetric characteristics but also high spatial content. Thus, the notion of geometrical structures and heterogeneous textures within VHR PolSAR data becomes more and more significant. Moreover, when the spatial resolution is increased, we need to deal with large-size image data. In this work, our motivation is to characterize textures by incorporating (fusing) both polarimetric and structural features, and then use them for classification purpose. First, polarimetric features from the weighted coherency matrix and local geometric information based on the Di Zenzo structural tensors are extracted and fused using the covariance approach. Then, supervised classification task is performed by using Riemannian distance measure relevant for covariance-based descriptors. In order to accelerate the computational time, we propose to perform texture description and classification only on characteristic points, not all pixels from the image. Experiments conducted on the VHR F-SAR data as well as the AIRSAR Flevoland image using the proposed framework provide very promising and competitive results in terms of terrain classification and discrimination.