In this paper, we target the problem of fracture classification from clinical X-Ray images towards an automated Computer Aided Diagnosis (CAD) system. Although primarily dealing with an image classification problem, we argue that localizing the fracture in the image is crucial to make good class predictions. Therefore, we propose and thoroughly analyze several schemes for simultaneous fracture localization and classification. We show that using an auxiliary localization task, in general, improves the classification performance. Moreover, it is possible to avoid the need for additional localization annotations thanks to recent advancements in weakly-supervised deep learning approaches. Among such approaches, we investigate and adapt Spatial Transformers (ST), Self-Transfer Learning (STL), and localization from global pooling layers. We provide a detailed quantitative and qualitative validation on a dataset of 1347 femur fractures images and report high accuracy with regard to inter-expert correlation values reported in the literature. Our investigations show that i) lesion localization improves the classification outcome, ii) weakly-supervised methods improve baseline classification without any additional cost, iii) STL guides feature activations and boost performance. We plan to make both the dataset and code available.