Grumier won the gold medal in the épée team event at the 2006 World Fencing Championships after beating Spain in the final. He accomplished this with his teammates Érik Boisse, Ulrich Robeiri and Fabrice Jeannet. He was also part of the French teams that won in 2010, 2011 and 2014. He won the silver medal in the individual épée event at the 2010 World Fencing Championships and at the 2015 World Fencing Championships.