This paper presents a TT-TFHE framework that efficiently performs homomorphic encryption inference of deep learning models using Torus FHE (TFHE). Based on a convolutional neural network called Truth-Table Neural Networks (TTnet), it effectively scales up the usage of TFHE for tabular and image datasets. It provides an open-source Concrete implementation in Python, and provides an easy CPU-based implementation using a lookup table and an automated TTnet-based design tool. Experimental results show that it outperforms existing homomorphic encryption settings in terms of time and accuracy on three tabular datasets, and outperforms other TFHE settings and other homomorphic encryption methods such as BFV and CKKS on MNIST and CIFAR-10 image datasets. In addition, it has a very small memory usage (tens of MB for MNIST), which contrasts with the tens to hundreds of GB of memory usage required by other homomorphic encryption settings. This is the first study to provide practical-level private inference (seconds of inference time, tens of MB of memory) on both tabular and MNIST image datasets, and is easily scalable to multiple threads and users on the server side.