We test the applicability of the Gallavotti-Cohen fluctuation formula on a non-equilibrium version of the periodic Ehrenfest wind-tree model. This is an one-particle system whose dynamics is rather complex (e.g., it appears to be diffusive at equilibrium), but its Lyapunov exponents are nonpositive. For small applied field, the system exhibits a very long transient, during which the dynamics is roughly chaotic, followed by asymptotic collapse on a periodic orbit. During the transient, the dynamics is diffusive, and the fluctuations of the current are found to be in agreement with the fluctuation formula, despite the lack of real hyperbolicity. These results also constitute an example which manifests the difference between the fluctuation formula and the EvansSearles identity.