Early and accurate prediction of cardiovascular disease is essential to improve patient outcomes and reduce healthcare costs. This research presents a hybrid classical–quantum machine learning framework for heart disease prediction using the Cleveland dataset. The proposed pipeline integrates advanced feature engineering, bio-inspired optimization, and quantum-inspired learning to improve classification performance and interpretability. The system applies multiple feature selection techniques followed by a hybrid feature fusion strategy. Orthogonal Component Analysis is then used for dimensionality transformation, while quantum-inspired feature mapping simulates quantum state coding. A feature selection mechanism based on a Genetic Algorithm optimizes the subset of features. Classical and quantum machine learning models are evaluated, including Random Forest, Gradient Boosting, K-Nearest Neighbors, Logistic Regression, Quantum Support Vector Classifier, Variational Quantum Classifier, Quantum KNN, and Quantum Neural Networks. Model performance is evaluated using accuracy metrics. To ensure transparency and trustworthiness, explainable AI techniques such as SHAP, LIME and DiCE are integrated to provide local and global interpretability of predictions. Experimental results demonstrate that the proposed hybrid framework improves predictive performance by achieving 90% accuracy compared to traditional machine learning approaches, while maintaining model explainability. The model achieved an overall accuracy of 90%, indicating strong predictive capability in cardiovascular disease risk classification. A detailed analysis of class-wise performance shows that for Class 0, the model obtained a precision of 0.85, a recall of 0.97, and an F1-score of 0.90, demonstrating excellent ability to correctly identify negative cases with minimal false negatives. For Class 1, the model achieved a precision of 0.96, a recall of 0.84, and an F1-score of 0.90, indicating high confidence in positive predictions, though with slightly lower recall compared to Class 0. This study highlights the potential of combining classical feature engineering, evolutionary optimization and quantum-inspired learning for next-generation medical decision support systems. The integration of quantum-inspired techniques also provides a promising direction for improving computational efficiency and model robustness in healthcare analytics. The findings suggest that hybrid classical–quantum learning approaches can support clinicians in making faster and more reliable diagnostic decisions.