Context. Early observations of comet C/2016 R2 (PanSTARRS) have shown that the composition of this comet is very peculiar. Radio observations have revealed a CO-rich and HCN-poor comet and an optical coma dominated by strong emission bands of CO+ and, more surprisingly, N2+ $\mathrm{N_2^+}$ N2+ . Aims. The strong detection of N2+ $\mathrm{N_2^+}$N2+ in the coma of C/2016 R2 provided an ideal opportunity to measure the 14N∕15N isotopic ratio directly from N2+ $\mathrm{N_2^+}$N2+ for the first time, and to estimate the N2∕CO ratio, which is an important diagnostic to constrain formation models of planetesimals, in addition to the more general study of coma composition. Methods. We obtained high resolution spectra of the comet in February 2018 when it was at 2.8 au from the Sun. We used the UVES spectrograph of the European Southern Observatory Very Large Telescope, complemented with narrowband images obtained with the TRAPPIST telescopes. Results. We detect strong emissions from the N2+ $\mathrm{N_2^+}$N2+ and CO+ ions, but also CO2+ $\mathrm{CO_2^+}$CO2+ , emission lines from the CH radical, and much fainter emissions of the CN, C2, and C3 radicals that were not detected in previous observations of this comet. We do not detect OH or H2O+, and we derive an upper limit of the H2O+∕CO+ ratio of 0.4, implying that the comet has a low water abundance. We measure a N2+/CO+ $\mathrm{N_2^+/CO^+}$N2+/CO+ ratio of 0.06 ± 0.01. The non-detection of NH2 indicates that most of the nitrogen content of the comet is in N2. Together with the high N2+/CO+ $\mathrm{N_2^+/CO^+}$N2+/CO+ ratio, this could indicate a low formation temperature of the comet or that the comet is a fragment of a large differentiated Kuiper Belt object. The CO2+/CO+ $\mathrm{CO_2^+/CO^+}$CO2+/CO+ ratio is 1.1 ± 0.3. We do not detect 14N15N+ lines and can only put a lower limit on the 14N∕15N ratio (measured from N2+ $\mathrm{N_2^+}$N2+ ) of about 100, which is compatible with measurements of the same isotopic ratio for NH2 and CN in other comets. Finally, in addition to the OI and CI forbidden lines, we detect for the first time the forbidden nitrogen lines NI doublet at 519.79 and 520.03 nm in the coma of a comet.