During the past decade, Deep Neural Networks (DNNs) proved their value on a large variety of subjects. However despite their high value and public accessibility, the protection of the intellectual property of DNNs is still an issue and an emerging research field. Recent works have successfully extracted fully-connected DNNs using cryptanalytic methods in hard-label settings, proving that it was possible to copy a DNN with high fidelity, i.e., high similitude in the output predictions. However, the current cryptanalytic attacks cannot target complex, i.e., not fully connected, DNNs and are limited to special cases of neurons present in deep networks. In this work, we introduce a new end-to-end attack framework designed for model extraction of embedded DNNs with high fidelity. We describe a new black-box side-channel attack which splits the DNN in several linear parts for which we can perform cryptanalytic extraction and retrieve the weights in hard-label settings. With this method, we are able to adapt cryptanalytic extraction, for the first time, to non-fully connected DNNs, while maintaining a high fidelity. We validate our contributions by targeting several architectures implemented on a microcontroller unit, including a Multi-Layer Perceptron (MLP) of 1.7 million parameters and a shortened MobileNetv1. Our framework successfully extracts all of these DNNs with high fidelity (88.4% for the MobileNetv1 and 93.2% for the MLP). Furthermore, we use the stolen model to generate adversarial examples and achieve close to white-box performance on the victim's model (95.8% and 96.7% transfer rate).