For this article, the interaction of tetrabutylammonium trifluoromethanesulfonate (TBATFO) with either fumaric (FUM) or maleic (MAL) acid has been investigated. These acids are isomers and can be considered the trans and cis configurations of the same molecular geometry. When TBATFO is mixed with FUM, an eutectic point is obtained for a relative composition of 90-10 (molar ratio), with a melting point of ≈90 °C. If maleic acid is mixed with TBATFO, one obtains an inhomogeneous phase with the retention of a solid portion immersed in a liquid phase, even above 90 °C. DFT calculations helped to model the interaction between the components. It is suggested herein that TBATFO interacts more strongly with FUM than with MAL, due to possible interactions in two different sites for hydrogen bonding (HB) in FUM. In MAL, one of the HB sites is instead retained in the intramolecular interactions; therefore, fewer sites are available for intermolecular interactions. Infrared spectroscopy measurements have confirmed this scenario, in which the hydrogen bonds of the acid molecules are replaced by HB between the acid and the ionic couple: for both kinds of mixtures, the vibration region of the OH bonds is strongly affected by mixing. However, in the case of FUM, the vibrations of the SO3 group of the TFO anion are displaced, while they remain in practically the same frequency position in the case of MAL.