CONUS+ is an experiment aiming at detecting coherent elastic neutrino-nucleus scattering (CEνNS) of reactor antineutrinos on germanium nuclei in the fully coherent regime, continuing the CONUS physics program conducted at the Brokdorf nuclear power plant (KBR), Germany. The CONUS+ experiment is installed in the Leibstadt nuclear power plant (KKL), Switzerland, at a distance of 20.7 m from the 3.6 GW reactor core, where the antineutrino flux is 1.5·1013 s-1 cm-2. The CEνNS signature will be measured with four point-contact high-purity low energy threshold germanium (HPGe) detectors. A good understanding of the background is crucial, especially events correlated with the reactor thermal power are troublesome, as they can mimic the predicted CEνNS interactions. A large background characterization campaign was conducted during reactor on and off times to find the best location for the CONUS+ setup. On-site measurements revealed a correlated, highly thermalized neutron field with a maximum fluence rate of (2.3±0.1)·104 neutrons d-1 cm-2 during reactor operation. The γ-ray background was studied with a HPGe detector without shield, paying special attention to the thermal power correlated 16N decay and other neutron capture γ-lines. The muon flux was examined using a liquid scintillator detector measuring (107 ± 3) muons s-1m-2, which corresponds to an average overburden of 7.4 m of water equivalent. The new background conditions in CONUS+ are compared to the previous CONUS ones, showing a 30 times higher flux of neutrons, but a 26 times lower component of reactor thermal power correlated γ-rays over 2.7 MeV. The lower CONUS+ overburden increases the number of muon-induced neutrons by 2.3 times and the flux of cosmogenic neutrons. Finally, all the measured rates are discussed in the context of the CONUS+ background, together with the CONUS+ modifications performed to reduce the impact of the new background conditions at KKL.