An aircraft has: an aircraft fuselage, a cabin region formed in the aircraft fuselage, underfloor region separated from the cabin region by a floor partition, and a fresh-water supply system. The fresh-water supply system has a fresh-water provision unit arranged in the underfloor region. The fresh-water supply system has multiple water extraction units which are each arranged in the cabin region, and a water line network branched off from the fresh-water provision unit and extending to the water extraction units. Each water extraction unit has a shut-off valve, a filter unit and a tapping point, which are coupled in series by means of water lines. Each filter unit has an exchangeable water filter with a first filter material designed for filtering particles out of the water flowing through the water filter and with a second filter material designed for softening the water flowing through the water filter.