Securing the exchange of health data is a critical challenge especially to safeguard the privacy and confidentiality of sensitive medical information. While many researchers have explored blockchain technology for secure storage and encryption in rapid data processing, there remains a significant gap in developing integrated solutions that effectively address privacy, scalability, and performance requirements in healthcare data exchange. To address this research gap, we propose the SAFE (Secure Access Framework for health-data Exchange) framework for health data sharing that integrates blockchain technology with symmetric encryption and contract-based access control. This framework ensures privacy, integrity, and immutability for both clinical data and medical images. The key contributions of this paper include an AES-based symmetric encryption algorithm, a contract-based access control mechanism, and a decryption and data utilization algorithm, designed to enable secure and efficient data sharing among authorized stakeholders. To validate the AES-based approach of SAFE, experiments have been conducted using the CBIS-DDSM breast cancer dataset to demonstrate that it outperforms alternative encryption methods—such as Symmetric Encryption with DES (Data Encryption Standard) and Blowfish (Twofish), and Asymmetric Encryption with RSA (Rivest-Shamir-Adleman) and ECC (Elliptic Cryptography)—in terms of encryption speed, decryption speed, and overall security, making it a viable solution for modern healthcare data exchange.