Deep Neural Networks (DNNs) show promising performance in several application domains, such as robotics, aerospace, smart healthcare, and autonomous driving. Nevertheless, DNN results may be incorrect, not only because of the network intrinsic inaccuracy, but also due to faults affecting the hardware. Indeed, hardware faults may impact the DNN inference process and lead to prediction failures. Therefore, ensuring the fault tolerance of DNN is crucial. However, common fault tolerance approaches are not cost-effective for DNNs protection, because of the prohibitive overheads due to the large size of DNNs and of the required memory for parameter storage. In this work, we propose a comprehensive framework to assess the fault tolerance of DNNs and cost-effectively protect them. As a first step, the proposed framework performs datatype-and-layer-based fault injection, driven by the DNN characteristics. As a second step, it uses classification-based machine learning methods in order to predict the criticality, not only of network parameters, but also of their bits. Last, dedicated Error Correction Codes (ECCs) are selectively inserted to protect the critical parameters and bits, hence protecting the DNNs with low cost. Thanks to the proposed framework, we explored and protected two Convolutional Neural Networks (CNNs), each with four different data encoding. The results show that it is possible to protect the critical network parameters with selective ECCs while saving up to 83% memory w.r.t. conventional ECC approaches.