Fourier transform infrared spectroscopy (FTIR) with Attenuated Total Reflection (ATR) combined with functional data analysis (FDA) was applied to differentiate aged wine spirits according to the ageing technology (traditional using 250 L wooden barrels versus alternative using micro-oxygenation and wood staves applied in 1000 L stainless steel tanks), the wood species used (chestnut and oak), and the ageing time (6, 12, and 18 months). For this purpose, several features of the wine spirits were examined: chromatic characteristics resulting from the CIELab method, total phenolic index, concentrations of furfural, ellagic acid, vanillin, and coniferaldehyde, and total content of low molecular weight phenolic compounds determined by HPLC. FDA applied to spectral data highlighted the differentiation between all groups of samples, confirming the differentiation observed with the analytical parameters measured. All samples in the test set were differentiated and correctly assigned to the aged wine spirits by FDA. The FTIR-ATR spectroscopy combined with FDA is a powerful methodology to discriminate wine spirits resulting from different ageing technologies.