NGC 1097 is a nearby SBb galaxy with a Seyfert nucleus and a bright starburst ring. We study the physical properties of the interstellar medium (ISM) in the ring using spatially resolved far-infrared spectral maps of the circumnuclear starburst ring of NGC 1097, obtained with the PACS spectrometer on board the Herschel Space Observatory. In particular, we map the important ISM cooling and diagnostic emission lines of OI 63 μm, OIII 88 μm, NII 122 μm, CII 158 μm and NII 205 μm. We observe that in the OI 63 μm, OIII 88 μm, and NII 122 μm line maps, the emission is enhanced in clumps along the NE part of the ring. We observe evidence of rapid rotation in the circumnuclear ring, with a rotation velocity of ~220 km s-1 (inclination uncorrected) measured in all lines. The OI 63 μm/CII 158 μm ratio varies smoothly throughout the central region, and is enhanced on the northeastern part of the ring, which may indicate a stronger radiation field. This enhancement coincides with peaks in the OI 63 μm and OIII 88 μm maps. Variations of the NII 122 μm/NII 205 μm ratio correspond to a range in the ionized gas density between 150 and 400 cm-3.