His older brother Benoît is Olympic champion from the K1 event at the 2004 Summer Olympics in Athens. Their father Claude is world champion in the K1 event from 1969.
He won five medals at the ICF Canoe Slalom World Championships with three golds (C1 team: 2007; C2 team: 2011, 2014), a silver (C1 team: 2009) and a bronze (C1 team: 2013). He also won eight medals at the European Championships (3 golds, 3 silvers and 2 bronzes).
Peschier won the overall World Cup title in the C2 class in 2012.