<p>Fréchet regression has emerged as a useful tool for modeling non-Euclidean response variables associated with Euclidean covariates. In this work, we propose a low-rank regularization approach for global Fréchet regression estimation, focusing on distributional response functions. We demonstrate that leveraging the low-rank structure of the model parameters enhances both the efficiency and accuracy of model fitting. Through theoretical analysis of the large-sample properties, we show that the proposed method enables more robust modeling and estimation than standard dimension reduction techniques. To support our findings, we also present numerical experiments that evaluate the finite-sample performance.</p>