The connection between two-dimensional Euclidean gravity and pure matrix models has lead to may fundamental insights about quantum gravity and string theory. The pure matrix model is thus a blueprint for the connection between discrete models and Euclidean quantum gravity. I will report on work with Astrid Eichhorn in which this "blueprint" model is investigated with the functional renormalization group. In this model, I will discuss the questions: "What is a possible meaning of asymptotic safety in a discrete model?" and "Is it possible to apply the FRGE to tensor models?