We present the discovery of TOI-3235 b, a short-period Jupiter orbiting an M dwarf with a stellar mass close to the critical mass at which stars transition from partially to fully convective. TOI-3235 b was first identified as a candidate from TESS photometry and confirmed with radial velocities from ESPRESSO and ground-based photometry from HATSouth, MEarth-South, TRAPPIST-South, LCOGT, and ExTrA. We find that the planet has a mass of 0.665 ± 0.025 M J and a radius of 1.017 ± 0.044 R J. It orbits close to its host star, with an orbital period of 2.5926 days but has an equilibrium temperature of ≈ 604 K, well below the expected threshold for radius inflation of hot Jupiters. The host star has a mass of 0.3939 ± 0.0030 M ☉, a radius of 0.3697 ± 0.0018 R ☉, an effective temperature of 3389 K, and a J-band magnitude of 11.706 ± 0.025. Current planet formation models do not predict the existence of gas giants such as TOI-3235 b around such low-mass stars. With a high transmission spectroscopy metric, TOI-3235 b is one of the best-suited giants orbiting M dwarfs for atmospheric characterization
