Direct imaging is an active research topic in astronomy for the detection and the characterization of young sub- stellar objects. The very high contrast between the host star and its companions makes detection particularly challenging. In addition to the use of an extreme adaptive optics system and a coronagraph to strongly attenuate the starlight contamination, dedicated post processing methods combining several images recorded with the pupil tracking mode of the telescope are needed. In previous works, we have presented the PACO algorithm capturing the spatial correlations of the data with a multi-variate Gaussian model whose parameters are estimated in a data-driven fashion at the scale of a patch of a few tens of pixels. PACO is parameter free and delivers reliable detection confidences with an improved sensitivity compared to the standard methods of the field. However, there is a room for improvement in the detection sensitivity due to the approximate fidelity of the PACO statistical model with respect to the observations. We propose to combine the statistics-based model of PACO with a deep learning approach in a three- step algorithm. First, the data are centered and whitened locally using the PACO framework to improve the stationarity and the contrast in a preprocessing step. Second, a convolutional neural network is trained in a supervised fashion to detect the signature of synthetic sources in the preprocessed science data. The network is trained from scratch with a custom data augmentation strategy allowing to generate a large training set from a single spatio-temporal dataset. Finally, the trained network is applied to the preprocessed observations and delivers a detection map. We apply our method on eleven datasets from the VLT/SPHERE-IRDIS instrument and compare our method with PACO and other baselines of the field (cADI, PCA). Our results show that the proposed method performs on-par with or better than these algorithms, with a contrast improvement up to half a magnitude with respect to PACO.