||Context. Feedback processes play a fundamental role in the regulation of the star formation (SF) activity in galaxies and, in particular, in the quenching of early-type galaxies (ETGs) as has been inferred by observational and numerical studies of Lambda -CDM models. At z=0, ETGs exhibit well-known fundamental scaling relations, but the connection between scaling relations and the physical processes shaping ETG evolution remains unknown.Aims. This work aims to study the impact of the energetic feedback due to active galactic nuclei (AGN) on the formation and evolution of ETGs. We focus on assessing the impact of AGN feedback on the evolution of the mass-plane and the fundamental plane (FP; defined using mass surface density) as well as on morphology, kinematics, and stellar age across the FP.Methods. The Horizon-AGN and Horizon-noAGN cosmological hydrodynamical simulations were performed with identical initial conditions, including the same physical processes except for the activation of the AGN feedback in the former. We selected a sample of central ETGs from both simulations using the same criteria and exhaustively studied their SF activity, kinematics, and scaling relations for z <= 3.Results. We find that Horizon-AGN ETGs identified at z=0 follow the observed fundamental scaling relations (mass-plane, FP, and mass-size relation) and qualitatively reproduce kinematic features albeit conserving a rotational inner component with a mass fraction regulated by the AGN feedback. We discover that AGN feedback seems to be required to reproduce the bimodality in the spin parameter distribution reported by observational works and the mass-size relation; more massive galaxies have older stellar populations, larger sizes, and are slower rotators. We study the evolution of the fundamental relations with redshift, finding a mild evolution of the mass-plane of Horizon-AGN ETGs for z< 1, whereas a stronger change is detected for z> 1. The ETGs in Horizon-noAGN show a strong systematic redshift evolution of the mass-plane. The FP of Horizon-AGN ETGs agrees with observations at z=0. When AGN feedback is switched off, a fraction of galaxies depart from the expected FP at all analysed redshifts owing to the presence of a few extended galaxies with an excess of stellar surface density. We find that AGN feedback regulates the SF activity as a function of stellar mass and redshift being able to reproduce the observed relations. Our results show the impact of AGN feedback on the mass-to-light ratio (M/L) and its relation with the tilt of the luminosity FP (L-FP; defined using the averaged surface brightness). Overall, AGN feedback has an impact on the regulation of the SF activity, size, stellar surface density, stellar ages, rotation, and masses of ETGs that is reflected on the fundamental relations, particularly on the FP. We detect a dependence of the FP on stellar age and galaxy morphology that evolves with redshfit. The characteristics of the galaxy distribution on the FP according to these properties change drastically by z similar to 1 in Horizon-AGN and hence this feature could provide further insight into the action of AGN feedback.