This paper introduces a robust and secure multimodal biometric recognition system that integrates facial and iris modalities using deep learning and advanced fusion techniques. Two pre-trained ResNet50 convolutional neural networks are independently employed to extract high-level discriminative features from face and iris images. To effectively utilize the complementary nature of these modalities, the extracted features are combined using both feature-level and score-level fusion strategies. Principal Component Analysis (PCA) is applied to reduce the dimensionality of the fused feature vectors while preserving critical variance. The reduced features are then classified using a range of machine learning algorithms, including Support Vector Machine (SVM), Decision Tree (DT), K-Nearest Neighbors (KNN), and Random Tree (RT). Experimental evaluations on benchmark datasets reveal that the proposed system achieves exceptional recognition performance, with the Random Tree classifier attaining a peak accuracy of 99.96% across both fusion approaches. Furthermore, the system achieves better results than several recent state-of-the-art methods in terms of accuracy, precision, recall, and F1-score. These results demonstrate the effectiveness, reliability, and scalability of the proposed framework for high-security biometric applications.