Alzheimer's disease (AD) is a progressive neurodegenerative disorder characterized by cognitive decline and functional impairment. Early detection is crucial for effective management and intervention. This study explores the effectiveness of an integrated deep learning approach combining convolutional neural networks (CNNs) and recurrent neural networks (RNNs) to enhance the early detection of Alzheimer's disease using multimodal data. A novel deep learning model was developed and validated, integrating neuroimaging data (MRI and PET scans) with clinical data using a decision-level fusion strategy. The study utilized a dataset comprising 1000 anonymized patient records from the Alzheimer’s Disease Neuroimaging Initiative (ADNI). Models were assessed based on accuracy, precision, recall, F1-score, and area under the receiver operating characteristic (ROC) curve (AUC). The integrated model demonstrated superior performance with an accuracy of 95%, precision of 94%, recall of 93%, and an F1-score of 93.5%. The model's AUC was 0.97, indicating excellent diagnostic capability. The proposed deep learning approach significantly improves the early detection of Alzheimer’s disease by effectively analyzing complex, multimodal data. This model holds considerable potential for clinical applications, providing a robust tool for healthcare professionals to diagnose AD in its early stages.