Ensuring fairness in the utilization of government-funded public facilities, such as co-working spaces, sports fields, and meeting rooms, is imperative to accommodate all citizens. However, meeting these requirements poses a significant challenge due to the high costs associated with maintaining digital infrastructure, employee wages, and cybersecurity expenses. Fortunately, Blockchain smart contracts present an economical and secure solution for managing digital infrastructure. They offer a pay-per-transaction schema, immutable transaction records, and role-based data updates. Despite these advantages, public blockchains raise concerns about data privacy since records are publicly readable. To address this issue, this study proposes a privacy-preserving mechanism for public facilities' reservation systems. The approach involves encrypting the reservation table with fully-homomorphic encryption (FHE). By employing FHE with binary masking and polynomial evaluation, the reservation table can be updated without decrypting the data. Consequently, citizens can discreetly book facilities without revealing their identities and eliminating the risk of overlapping schedules. The proposed system allows anyone to verify reservations without disclosing requested data and table contents. Moreover, the system operates autonomously without the need for human administration, ensuring enhanced user privacy.