Abstract: We report the discovery and characterisation of a giant transiting planet orbiting a nearby M3.5V dwarf (d = 80.4pc, G = 15.1 mag, K=11.2mag, R-* = 0.358 +/- 0.015 R-circle dot, M-* = 0.340 +/- 0.009 M-circle dot). Using the photometric time series from TESS sectors 10, 36, 46, and 63 and near-infrared spectrophotometry from ExTrA, we measured a planetary radius of 0.77 +/- 0.03 R-J and an orbital period of 1.52 days. With high-resolution spectroscopy taken by the CFHT/SPIRou and ESO/ESPRESSO spectrographs, we refined the host star parameters ([Fe/H] = 0.27 +/- 0.12) and measured the mass of the planet (0.273 +/- 0.006 M-J). Based on these measurements, TOI-4860 b joins the small set of massive planets (>80 M-E) found around mid to late M dwarfs (<0.4 R-circle dot), providing both an interesting challenge to planet formation theory and a favourable target for further atmospheric studies with transmission spectroscopy. We identified an additional signal in the radial velocity data that we attribute to an eccentric planet candidate (e = 0.66 +/- 0.09) with an orbital period of 427 +/- 7 days and a minimum mass of 1.66 +/- 0.26 M-J, but additional data would be needed to confirm this.