Analyses of lunar samples suggest the Moon once possessed a dynamo from similar to 4.25 Ga until perhaps as recently as 1 Ga, with surface field strengths between similar to 5 and 100 mu T. While the exact timing, strength, and structure of these paleomagnetic fields are not precisely known, such relatively strong fields imply that the Moon also likely possessed a magnetosphere. Here, we present hybrid plasma simulations of the structure and morphology of the putative lunar paleo-magnetosphere for varying surface field strengths and orientations, using ambient solar wind conditions representative of the early Sun. The presence of the paleo-magnetosphere reduces total solar wind fluxes to the lunar surface overall yet, for a spin-aligned dynamo, increases the relative solar wind flux to the lunar polar regions. In turn, the paleo-magnetosphere may have altered the rate of volatile accretion to the Moon over its history.