Skin disease classification is a complex task that requires robust feature extraction, efficient classification, and interpretability. Artificial intelligence-based technologies offer effective solutions for developing a framework for skin disease classification while ensuring explainability for healthcare professionals. This study proposes a novel Hybrid Transformer model comprising of Convolutional Neural Network (CNN) architecture infused with a Quantum-Inspired Fourier Transform (QIFT) to enhance classification accuracy. QIFT is incorporated to emphasize frequency-domain information alongside the spatial features captured by CNNs, potentially improving feature representation and model generalization. For demonstration, a dataset containing four different classes of dermatological images is used. Data augmentation techniques and adaptive learning rate scheduling are employed to optimize the dataset. A weighted cross-entropy loss function is used to address class imbalances in the dataset. In this research, explainability is implemented using a standard attribution technique like Integrated Gradients providing insights into model decision-making, and enhancing trust in medical applications. Performance evaluation involves validating the proposed framework using metrics such as confusion matrix analysis, classification reports, and training-validation curves. Experimental results demonstrate a high classification accuracy of 92.5% across skin disease categories. The findings indicate that integrating QIFT and CNN-based feature extraction with transformer-driven attention mechanisms enhances skin disease classification performance while ensuring interpretability as process innovation.