The impressive performance of deep learning models, particularly Convolutional Neural Networks (CNNs), is often hindered by their lack of interpretability, rendering them "black boxes." This opacity raises concerns in critical areas like healthcare, finance, and autonomous systems, where trust and accountability are crucial. This paper introduces the QIXAI Framework (Quantum-Inspired Explainable AI), a novel approach for enhancing neural network interpretability through quantum-inspired techniques. By utilizing principles from quantum mechanics, such as Hilbert spaces, superposition, entanglement, and eigenvalue decomposition, the QIXAI framework reveals how different layers of neural networks process and combine features to make decisions. We critically assess model-agnostic methods like SHAP and LIME, as well as techniques like Layer-wise Relevance Propagation (LRP), highlighting their limitations in providing a comprehensive view of neural network operations. The QIXAI framework overcomes these limitations by offering deeper insights into feature importance, inter-layer dependencies, and information propagation. A CNN for malaria parasite detection is used as a case study to demonstrate how quantum-inspired methods like Singular Value Decomposition (SVD), Principal Component Analysis (PCA), and Mutual Information (MI) provide interpretable explanations of model behavior. Additionally, we explore the extension of QIXAI to other architectures, including Recurrent Neural Networks (RNNs), Long Short-Term Memory (LSTM) networks, Transformers, and Natural Language Processing (NLP) models, and its application to generative models and time-series analysis. The framework applies to both quantum and classical systems, demonstrating its potential to improve interpretability and transparency across a range of models, advancing the broader goal of developing trustworthy AI systems.