Gaussian tensor networks are a special class of quantum circuits which are also single-particle basis transformations and map an entangled, non-interacting fermionic state to an unentangled state. We show that Gaussian tensor networks can be useful for interacting systems too. Although they no longer map to an unentangled state in the presence of interactions, applying them to an interacting system can greatly reduce its entanglement. The basis transformation defined by a Gaussian tensor network can be applied to the Hamiltonian before doing any many-body computations, avoiding working with the original, highly-entangled state. We explore applications of different types of Gaussian tensor networks to impurity model systems and consider applications to computing ground state and dynamical properties.