In this article, we propose a new generalized framework, termed an F-modular bcomplete metric space, which naturally combines the features of modular metric spaces, b-metric spaces, and F-metric spaces. This structure allows a unified treatment of several distance-type notions that have appeared independently in the literature. Within this setting, we establish analogues of classical fixed point results, including Banach, Kannan, Chatterjea, and several rational-type contraction principles for self-mappings. The obtained results extend and refine many existing fixed point theorems in generalized metric spaces. To illustrate the applicability of the proposed framework, one of the derived fixed point theorems is used to establish the existence and uniqueness of a solution of a nonlinear integral equation.