This research proposes "ForCM", a novel approach to forest cover mapping that combines Object-Based Image Analysis (OBIA) with Deep Learning (DL) using multispectral Sentinel-2 imagery. The study explores several DL models, including UNet, UNet++, ResUNet, AttentionUNet, and ResNet50-Segnet, applied to high-resolution Sentinel-2 Level 2A satellite images of the Amazon Rainforest. The datasets comprise three collections: two sets of three-band imagery and one set of four-band imagery. After evaluation, the most effective DL models are individually integrated with the OBIA technique to enhance mapping accuracy. The originality of this work lies in evaluating different deep learning models combined with OBIA and comparing them with traditional OBIA methods. The results show that the proposed ForCM method improves forest cover mapping, achieving overall accuracies of 94.54 percent with ResUNet-OBIA and 95.64 percent with AttentionUNet-OBIA, compared to 92.91 percent using traditional OBIA. This research also demonstrates the potential of free and user-friendly tools such as QGIS for accurate mapping within their limitations, supporting global environmental monitoring and conservation efforts.