The recent Far-Infrared Polarimetric Large-Area Central Molecular Zone Exploration (FIREPLACE) survey with SOFIA has mapped plane-of-sky magnetic field orientations within the Central Molecular Zone (CMZ) of the Milky Way. Applying the Histogram of Relative Orientations analysis to the FIREPLACE data, we find that the relative orientation between magnetic fields and column density structures is random in low-density regions ( 2x1022 less than or similar to NH2 less than or similar to 1023cm-2 ) but becomes preferentially parallel in high-density regions (greater than or similar to 1023 cm-2). This trend is in contrast with that of the nearby molecular clouds, where the relative orientation transitions from parallel to perpendicular with increasing column densities. However, the relative orientation varies between individual CMZ clouds. Comparisons with magnetohydrodynamic simulations specific to the CMZ conditions suggest that the observed parallel alignment is intrinsic, rather than artifacts caused by the projection effect. The origin of this parallel configuration may arise from the fact that most dense structures in the CMZ are not self-gravitating, as they are in supervirial states, except for the ministarburst region Sgr B2. These findings are consistent with the low star formation efficiency observed in the CMZ compared to that in the Galactic disk.