File fragment type identification is an important step in file carving and data recovery. Machine learning techniques, especially neural networks, have been utilized for this problem, some with very promising results. This paper presents a novel neural network architecture for identifying file fragment types using a combination of byte embeddings as well as recurrent and convolutional elements. The corresponding classification model, ByteRCNN, has been trained on the publicly available file fragment FiFTy dataset and evaluated in closed-set and open-set recognition settings using FiFTy and other available file fragment datasets. Evaluation results have demonstrated that ByteRCNN can compete with state-of-the-art models described in literature in terms of classification accuracy, with 71.1% average accuracy on 512-byte fragments and 83.9% average accuracy on 4,096-byte fragments from the FiFTy dataset. When evaluated on other publicly available datasets in closed-set and open-set recognition settings, ByteRCNN similarly or slightly better than the FiFTy classification model. Obtained results overall suggest that ByteRCNN is a competitive file fragment classification model, but they also reveal that there is still plenty of space for further improving file type identification methods using more complex datasets or in open-set recognition settings. ByteRCNN is publicly available at [GitHub, after publication].