Context. N2 is rarely found in comets, or when it is present, it is found only in small quantities despite its abundance on the surfaces of different outer Solar System objects. A few comets presented N2+ emission lines in their optical spectra. One of them, C/2016 R2, showed an unusually high abundance of this species in 2018, with dozens of bright N2+ emission lines. A robust model of the N2+ fluorescence in comets would permit us to perform a detailed quantitative analysis of this species and enlarge our comprehension of the surprisingly wide range of N2 abundances in comets.Aims. The goal of this work is to provide the necessary tools to interpret N2+ spectra. Computing production rates for a cometary species necessitates a good knowledge of the number of molecules located along the line of sight of the spectrometer. This in turn requires a good modeling of the emission spectrum with detailed fluorescence efficiencies for the different bands.Methods. We developed a model based on available laboratory data and new theoretical results relative to the N2+ to compute the emission spectrum of this species observed in 8.2m Very Large Telescope high-resolution spectra of comet C/2016 R2. Because of some significant differences between spectra obtained on the nucleus and at a cometocentric distance of about 6000 km, it became apparent that a classic fluorescence equilibrium spectrum could not be used. A synthetic spectrum based on a Monte Carlo method and producing spectra at different times from an initial relative population was developed and compared to our observational data.Results. Our modeling of the cometary N2+ emission spectrum satisfactorily fits our observed spectra of comet C/2016 R2, leading to the first modeling at high resolution. Different fluorescence efficiency factors are computed.