This paper presents TT-TFHE, a deep neural network Fully Homomorphic Encryption (FHE) framework that effectively scales Torus FHE (TFHE) usage to tabular and image datasets using a recent family of convolutional neural networks called Truth-Table Neural Networks (TTnet). The proposed framework provides an easy-to-implement, automated TTnet-based design toolbox with an underlying (python-based) open-source Concrete implementation (CPU-based and implementing lookup tables) for inference over encrypted data. Experimental evaluation shows that TT-TFHE greatly outperforms in terms of time and accuracy all Homomorphic Encryption (HE) set-ups on three tabular datasets, all other features being equal. On image datasets such as MNIST and CIFAR-10, we show that TT-TFHE consistently and largely outperforms other TFHE set-ups and is competitive against other HE variants such as BFV or CKKS (while maintaining the same level of 128-bit encryption security guarantees). In addition, our solutions present a very low memory footprint (down to dozens of MBs for MNIST), which is in sharp contrast with other HE set-ups that typically require tens to hundreds of GBs of memory per user (in addition to their communication overheads). This is the first work presenting a fully practical solution of private inference (i.e. a few seconds for inference time and a few dozens MBs of memory) on both tabular datasets and MNIST, that can easily scale to multiple threads and users on server side.