Context. Carbon fractionation has been studied from a theoretical point of view with different models of time-dependent chemistry, including both isotope-selective photodissociation and low-temperature isotopic exchange reactions. Aims. Recent chemical models predict that isotopic exchange reactions may lead to a depletion of ¹³C in nitrile-bearing species, with ¹²C/¹³C ratios two times higher than the elemental abundance ratio of 68 in the local interstellar medium. Since the carbon isotopic ratio is commonly used to evaluate the ¹⁴N/¹⁵N ratios with the double-isotope method, it is important to study carbon fractionation in detail to avoid incorrect assumptions. Methods. In this work, we implemented a gas-grain chemical model with new isotopic exchange reactions and investigated their introduction in the context of dense and cold molecular gas. In particular, we investigated the ¹²C/¹³C ratios of HNC, HCN, and CN using a grid of models, with temperatures and densities ranging from 10 to 50 K and 2 × 10³ to 2 × 10⁷ cm⁻³, respectively. Results. We suggest a possible ¹³C exchange through the ¹³C + C₃ → ¹²C +¹³CC₂ reaction, which does not result in dilution, but rather in ¹³C enhancement, for molecules that are formed starting from atomic carbon. This effect is efficient in a range of time between the formation of CO and its freeze-out on grains. Furthermore, the parameter-space exploration shows, on average, that the ¹²C/¹³C ratios of nitriles are predicted to be a factor 0.8–1.9 different from the local ¹²C/¹³C of 68 for high-mass star-forming regions. This result also affects the ¹⁴N/¹⁵N ratio: a value of 330 obtained with the double-isotope method is predicted to vary in the range 260–630, up to 1150, depending on the physical conditions. Finally, we studied the ¹²C/¹³C ratios of nitriles by varying the cosmic-ray ionisation rate, ζ: the ¹²C/¹³C ratios increase with ζ because of secondary photons and cosmic-ray reactions.