Nuclear reactions drive the stellar evolution and contribute to the stellar and galactic chemicals abundances. New determinations of the nuclear reaction rates for key fusion reactions of stellar evolution are now available, paving the way to improved stellar model predictions. We explore the impact of new C12+C12 reaction rates for massive stars evolution, structure, and nucleosynthesis during core carbon-burning phase. We analyse the consequences for stars of different masses including rotation-induced mixing. We computed a grid of massive stars at solar metallicity using the stellar evolution code GENEC. We explored the results using three different references for the rates, with or without rotation. We study the effect in terms of evolution, structure, and critical mass limit between intermediate and massive stars. We explored the consequences for nucleosynthesis during the core C-burning phase by means of a one-zone nucleosynthesis code. We confirm the significant impact of using the recent nuclear reaction rates following the hindrance hypothesis as well as the mass-dependent effect of a resonance at 2.14 MeV. This impacts the characteristics of the core of stars from the C-ignition and during all the core C-burning phase. The change of rates modifies the central nucleosynthesis during the core C-burning phase, resulting in an underproduction of s-process elements. The correct and accurate determination of the nuclear reaction rates, with especially the existence and location of resonances, impacts stellar evolution in many aspects affecting the model predictions. The choice of the nuclear reaction rates reference for the C12+C12 fusion reaction changes significantly the behaviour of the core during the C-burning phase. This choice is then to be taken carefully in order to interpret stellar evolution and fate of massive stars.