<p>This paper focuses on the effective dynamics of a class of stochastic parabolic equations with a fast oscillation driven by fractional Brownian motion and Poisson jumps under non-Lipschitz conditions. This model is designed to describe systems that exhibit long-range dependence and emergency impact. In this work, we demonstrate the tightness of the slow component and the ergodicity of the fast component. Furthermore, it is shown that the slow component converges to the solution of the corresponding effective equation. The averaging principle simplifies the computational complexity, enabling us to bypass the intricacies of the original system and instead focus on analyzing the behavior of the effective equation. In contrast to studies that rely on Lipschitz conditions, the results presented here extend beyond these restrictions by considering non-Lipschitz conditions, which are more flexible and widely applicable.</p>