Ensuring secure and privacy-preserving authentication in web applications remains a critical challenge due to the limitations of conventional single-factor approaches, which are vulnerable to attacks and fail to account for dynamic user behaviors. Existing multi-factor authentication (MFA) methods often rely on static rules, exposing users to unnecessary friction or weak security under evolving threat conditions. To address these gaps, this study proposes PPAB-RL, a Privacy-Preserving Adaptive Biometric framework leveraging Reinforcement Learning for intelligent MFA selection. The proposed method integrates homomorphic encryption for secure fingerprint feature storage, contextual risk scoring based on device, behavioral, and geolocation deviations, and RL-driven adaptive MFA to dynamically select authentication pathways from password-only to multi-step biometric verification. Implementation is carried out using Python, with biometric processing performed on the SOCOFing dataset containing 6,000 fingerprint images, and blockchain-enabled logging for immutable and tamper-proof audit trails. Experimental results demonstrate that PPAB-RL achieves 96.8 authentication accuracy, surpassing traditional password-only (84.2) and fingerprint-only (93.5) methods, while maintaining low encrypted matching overhead and minimal user friction. Ablation studies confirm the essential contribution of each module, biometric preprocessing, encryption, risk analysis, and RL-based adaptation to overall system robustness. The RL policy converges rapidly, allowing real-time adaptation to changing user behaviors and threat contexts. Overall, the proposed PPAB-RL framework establishes a highly secure, intelligent, and scalable authentication paradigm, combining encrypted biometrics, dynamic risk assessment, and blockchain validation, offering an innovative approach that can inspire further research in next-generation privacy-sensitive authentication systems.