We present MeerKAT observations of neutral hydrogen gas (H I) in the nearby merger remnant NGC 1316 (Fornax A), the brightest member of a galaxy group which is falling into the Fornax cluster. We find H I on a variety of scales, from the galaxy centre to its large-scale environment. For the first time we detect H I at large radii (70-150 kpc in projection), mostly distributed on two long tails associated with the galaxy. Gas in the tails dominates the H I mass of NGC 1316: 7 × 108 M☉- 14 times more than in previous observations. The total H I mass is comparable to the amount of neutral gas found inside the stellar body, mostly in molecular form. The H I tails are associated with faint optical tidal features thought to be the remnant of a galaxy merger occurred a few billion years ago. They demonstrate that the merger was gas-rich. During the merger, tidal forces pulled some gas and stars out to large radii, where we now detect them in the form of optical tails and, thanks to our new data, H I tails; while torques caused the remaining gas to flow towards the centre of the remnant, where it was converted into molecular gas and fuelled the starburst revealed by the galaxy's stellar populations. Several of the observed properties of NGC 1316 can be reproduced by a ̃10:1 merger between a dominant, gas-poor early-type galaxy and a smaller, gas-rich spiral occurred 1-3 Gyr ago, likely followed by subsequent accretion of satellite galaxies.