The Lorraine-Saar Basin is one of the largest geologically and commercially important Palaeozoic coal-bearing basins in Central Europe, which has considerable coal reserves in numerous coal beds. Geologically, the Lorraine Basin stands out by its up to 5 km sedimentary column and its inversion resulting in Paleozoic low-amplitude erosion in the range of 750 m (French part of the basin) and pre-Mesozoic (Permian) erosion between 1800 and 3000 m (the Saar coalfield or German part of the basin). Thermal maturation of wide spectra of organic-rich-matter ranging from dispersed organic matter in sedimentary clastic rocks to concentrated organic matter in coal seams has led to the formation of enormous coalbed methane (CBM) resource in many domains throughout the Carboniferous Westphalian and Stephanian sequences. Coal mines here are no longer operated to produce coal; however, gas generated in "dry gas window" compartments at a depth exceeding 3.5 km have escaped here via several major faults and fracture corridors forming "sweet spots gas" sites. Faults, a dense network of tectonic fractures together with post-mining subsidence effects also increased the permeability of a coal-bearing massive and provided pathways for the breathing of environmentally hazardous mine gases. Nearly all CBM plays can be classified as naturally fractured reservoirs. The Lorraine-Saar Basin is not exclusion indeed because of the long-term experience of industrial geological surveys during underground coal-mining in the past. The knowledge of geometrical features of fracture and cleat patterns is a crucial parameter for determining the absolute permeability of a resource play, its kinematics environment, and further reservoir simulation. The main focus of this contribution is to get an insight into the style and structural trends of natural fracture and cleat patterns in the basin based on the results of X-ray computer tomography (CT) to ensure proper technical decisions for efficient exploration and exploitation of coalbed methane reservoirs. To explore the architecture of solid coal samples we used X-ray computed tomography of coal specimen collected from the Westphalian D coal seam 10 of exploratory well Tritteling 1. The studied coal specimen (principle sample) and its 2 local subvolumes were inspected in 3 series of experiments (with resolutions of 30, 10, and 2 µm). At different levels of X-ray CT, we identified two quasi-orthogonal cleat systems including a smooth-sided face cleat of tensile origin and a curvilinear shearing butt cleat. The inferred tectonic zones, discrete fractures, and tectonically induced cleat patterns clearly possess features of self-similarity and usually align with directional stresses. Results of the treatment of obtained cleat patterns in terms of their connectivity relationship allowed distinguishing the presence within studied samples interconnected cleat arrays potentially facilitating success in CBM extraction projects.