Detecting breast cancer at an early stage remains a pressing challenge in medical diagnostics, where advancements can significantly impact patient outcomes. This work proposes a hybrid model combining Convolutional Neural Networks (CNNs) and Support Vector Machines (SVMs) optimized for clinical data analysis. By leveraging CNNs for automatic feature extraction and SVMs for precise classification, our approach integrates a soft voting mechanism to achieve an accuracy of 98.2%, minimizing false negatives—a critical metric in healthcare. Additionally, the model demonstrates robustness across diverse datasets and effectively manages class imbalances. This hybrid methodology underscores its potential as a reliable diagnostic tool in clinical environments.