Neveu won ten medals at the ICF Canoe Slalom World Championships with three golds (K1: 2014; K1 team: 2006, 2014), six silvers (K1: 2009, K1 team: 2010, 2011, 2017, Extreme K1: 2017, 2018) and a bronze (K1 team: 2013). He also won eight medals at the European Championships (3 golds, 3 silvers and 2 bronzes).