The rising frequency of data breaches and unauthorized access in healthcare systems has heightened concerns over privacy protection in Electronic Health Records (EHRs), especially when third parties, such as insurance companies, are involved. Traditional EHR solutions are often inadequate in safeguarding data confidentiality during multi-user access. This paper presents the Blockchain-based Smart Medical Privacy-preserving Contract System (BSMPCS), a novel framework designed to address these privacy challenges. By integrating Bitcoin smart contracts and homomorphic encryption, BSMPCS ensures secure management of EHRs while restricting access to only authorized entities. The decentralized and immutable characteristics of blockchain enhance data integrity, while smart contracts prevent unauthorized disclosure of sensitive health information to insurance companies. Additionally, homomorphic encryption enables insurance claim verifications without exposing the actual health records, preserving both patient identity and medical privacy. Unlike conventional systems, BSMPCS eliminates the need for third-party intermediaries, significantly reducing the risk of data leaks. Combining blockchain and advanced cryptographic methods, this framework provides a robust, privacy-preserving solution suitable for modern healthcare systems.