We demonstrate a fibre-based approach that generates mid-infrared femtosecond pulses in the 3-4 µm spectral region with microjoule-level single pulse energy. This is realised in a piece of gas-filled antiresonant hollow-core fibre that is pumped by a two-micron light source. A rapid variation of the dispersion near a structural resonance of the fibre creates a phase-matching point in the mid-infrared, which mediates the frequency-down conversion. We generate femtosecond pulses centred at 3.16 µm wavelength with the pulse energy of more than 1 µJ, achieving the conversion efficiency as high as 9.4 %. The wavelength of the radiation is determined solely by the dielectric wall thickness of the cladding elements, while the yield is subject to other experimental parameters. This, combined with high power-handling capability of hollow-core fibres, makes it possible to power scale the mid-infrared output by either increasing the pulse energy or repetition rate of the pump. The technique presents a new pathway to build an allfibre-based mid-infrared supercontinuum source, which promises to be a powerful new tool for ultrahigh sensitivity molecular spectroscopy.