Fractures, which are related to tectonic activity and lithology, have a significant impact on the storage and production of oil and gas in shales. To analyze the impact of lithological factors on fracture development in shales, we selected the shale formation from the Da’anzhai member of the lower Jurassic shales in a weak tectonic deformation zone in the Sichuan Basin. We defined a lithology combination index (LCI), that is, an attribute quantity value of some length artificially defined by exploring the lithology combination. LCI contains information on shale content at a certain depth, the number of layers in a fixed length (lithology window), and the shale content in the lithology window. Fracture porosity is the percentage of pore volume to the apparent volume of the rock. In the experiment, fracture porosity was obtained using 50 samples from six wells, by observing rock slices under a microscope. The relationship between LCI and fracture porosity was analyzed based on machine learning, regression analysis, and weighting methods. The results show that LCI is able to represent the impact of multiple lithological factors (i.e., shale content at a certain depth, the number of layers in the lithology window, and the shale content in the lithology window). The LCI within a thickness of 2 m for the lithology window demonstrates a good linear relationship with fracture porosity. We therefore suggest LCI be used for fracture predictions of shale formations from weak tectonic deformation zones. Our proposed LCI and fracture prediction methods also provide implications for sandstone, mudstone, or carbonate formations under similar processes.