Context. The millimetre spectrum of Galactic regions and galaxies is rich in continuum and molecular lines. This diversity is mostly explored using either broad-band photometry or high-resolution heterodyne spectroscopy. Aims. We aim to map the millimetre continuum emission of Galactic regions with an intermediate spectral resolution between broadband photometry and heterodyne spectroscopy, enabling us to rapidly cover large sky areas with spectroscopy. Methods. We report observations of the Orion Nebula with the CONCERTO instrument, which was installed at the APEX telescope focal plane from 2021 to 2023. Results. We find that the spectrum of Orion is dominated by dust emission with an emissivity index ranging between 1.3 and 2.0, along with strong CO(2-1) and H2O lines, which are naturally separated from the continuum due to the CONCERTO spectral capabilities. Many regions also show strong free-free emission at lower frequencies. Conclusions. We demonstrate the spectral capabilities of CONCERTO at intermediate spectral resolution, with a frequency coverage from 130 to 310 GHz. A sensitivity of 200 mK is achieved in one second, for one beam and a 6 GHz frequency width, over an 18 arcmin diameter field of view, which is within a factor of three of the expectations. We show that we can spectrally disentangle the continuum from the CO line emission, but the line is not resolved at a resolution of ~8000 km s–1. The slope of the millimetre continuum is line-free mapped for the first time in Orion.