Quantum computing poses existential risks to classical encryption in cloud forensics, threatening evidence integrity and legal admissibility. This study presents a new security system for cloud forensics called the Quantum-Resilient Cloud Forensic Security Framework (QRCFSF), which uses Quantum Key Distribution (QKD) and AI to detect unusual activities, helping to solve current and future problems related to quantum computing. Simulations of the BB84 QKD protocol produced a sifted key rate of 50.2 bits. They detected eavesdropping in ideal conditions 98.9% of the time, which is better than classical methods that are at risk from Shor's algorithm. The framework uses QKD for secure authentication and a mix of AI techniques (Random Forest, LSTM, Isolation Forest), reaching 97.1% accuracy in spotting unusual activities and only 1.2% false alarms in mixed forensic data. NIST SP 800–207 (Zero Trust) and ISO 27037 compliance is guaranteed by blockchain timestamping and GDPR-compliant pseudonymization. Real-world scalability is addressed by hybrid QKD-Post-Quantum Cryptography (PQC) architectures and decoy-state protocols. The findings give forensic investigators practical advice on protecting cloud systems from future quantum decryption attacks.