Multispectral imaging satellites such as Sentinel-2 are considered a possible tool to assist in the mapping of soil organic carbon (SOC) using images of bare soil. However, the reported results are variable. The measured reflectance of the soil surface is not only related to SOC but also to several other environmental and edaphic factors. Soil texture is one such factor that strongly affects soil reflectance. Depending on the spatial correlation with SOC, the influence of soil texture may improve or hinder the estimation of SOC from spectral data. This study aimed to investigate these influences using local models at 34 sites in different pedo-climatic zones across 10 European countries. The study sites were individual agricultural fields or a few fields in close proximity. For each site, local models to predict SOC and the clay particle size fraction were developed using the Sentinel-2 temporal mosaics of bare soil images. Overall, predicting SOC and clay was difficult, and prediction performances with a ratio of performance to deviation (RPD) > 1.5 were observed at 8 and 12 of the 34 sites for SOC and clay, respectively. A general relationship between SOC prediction performance and the correlation of SOC and clay in soil was evident but explained only a small part of the large variability we observed in SOC prediction performance across the sites. Adding information on soil texture as additional predictors improved SOC prediction on average, but the additional benefit varied strongly between the sites. The average relative importance of the different Sentinel-2 bands in the SOC and clay models indicated that spectral information in the red and far-red regions of the visible spectrum was more important for SOC prediction than for clay prediction. The opposite was true for the region around 2200 nm, which was more important in the clay models.