Fuzzy closure spaces are an extension of classical closure spaces in topology, where the concept of closure is defined in terms of fuzzy sets. This article introduces interior operators and neighborhood systems in fuzzy closure spaces. Using that, we have redefined ČF-continuity. Separation axioms such as ČFT0, ČFT1, and ČFT2, ČF-Urysohn, ČF-regular, and ČF-normal in fuzzy closure spaces are introduced using these neighborhood systems. Additive, productive, hereditary, and other properties of these axioms have been observed. Relationships between these axioms are also investigated.