Water based glues make the leather expand and wrinkle. Once dried it might not assume the shape you desire. Solvent adhesives (contact cement, which is used by leather workers) would more than likely react with the styrene center of the foamboard. Best to use something that is not permanent and reversible if possible (sewing, tag gun, etc.). Remember that leather contracts and expands with changes in relative humidity.
Question: is the entire piece of leather going to be seen (floated), or do you have margins that could be wrapped around a mount?