We present [C/Fe] and [N/Fe] abundance ratios and CH(λ4300) and S(λ3883) index measurements for 94 red giant branch (RGB) stars in the Sculptor dwarf spheroidal galaxy from VLT/VIMOS MOS observations at a resolving power R = 1150 at 4020 Å. This is the first time that [N/Fe] abundances are derived for a large number of stars in a dwarf spheroidal. We found a trend for the [C/Fe] abundance to decrease with increasing luminosity on the RGB across the whole metallicity range, a phenomenon observed in both field and globular cluster giants, which can be interpreted in the framework of evolutionary mixing of partially processed CNO material. Both our measurements of [C/Fe] and [N/Fe] are in good agreement with the theoretical predictions for stars at similar luminosity and metallicity. We detected a dispersion in the carbon abundance at a given [Fe/H], which cannot be ascribed to measurement uncertainties alone. We interpret this observational evidence as the result of the contribution of different nucleosynthesis sources over time to a not well-mixed interstellar medium. We report the discovery of two new carbon-enhanced, metal-poor stars. These are likely the result of pollution from material enriched by asymptotic giant branch stars, as indicated by our estimates of [Ba/Fe] >+1. We also attempted a search for dissolved globular clusters in the field of the galaxy by looking for the distinctive C-N pattern of second population globular clusters stars in a previously detected, very metal-poor, chemodynamical substructure. We do not detect chemical anomalies among this group of stars. However, small number statistics and limited spatial coverage do not allow us to exclude the hypotheses that this substructure forms part of a tidally shredded globular cluster. Based on observations made with ESO Telescopes at the La Silla Paranal Observatory under programme ID 091.D-0089