Distributed Brillouin optical fiber sensors can detect temperature and strain over long distances in standard single-mode fibers from the measurement of their Brillouin gain spectrum (BGS). However, the performance of these sensors is restricted by parameters such as the frequency scanning interval, average times of data acquisition, and Brillouin frequency shift (BFS) extraction time. Therefore, achieving high-precision real-time monitoring is challenging. In this study, we introduce a nonlinear interpolation deep neural network (NIDNN) to interpolate and denoise the BGS. Additionally, we propose a BFS extraction convolutional neural network (BFSECNN) based on depthwise separable convolution (DSC) to shorten the BFS extraction and training time. Both the simulation and experimental results show that the NIDNN and BFSECNN contributed to higher accuracy in BFS extraction and shorter data processing time. The sweep time of the distributed Brillouin optical fiber sensor with a 28.5-km length after using the NIDNN is 1/6 of the hardware sweep time of the 1-MHz interval, and the BFSECNN extraction time is 3.7 s. Moreover, combining the NIDNN with the BFSECNN reduced the BFS uncertainty by 5.3 MHz at the end of the optical fiber. Used individually or together, the proposed NIDNN and BFSECNN could improve the performance of existing distributed Brillouin optical fiber sensors without any hardware modifications.