Robeiri was born in Cayenne, French Guiana. He began fencing at age 8 at the Éclaireuses et Éclaireurs de France, an interreligious scouting association. He first practiced foil, the traditional learning weapon, before turning to épée. He first joined the centre for promising young athletes in Les Abymes, in Guadeloupe, then at the age of 15, the centre of Reims in metropolitan France. In 2001, he earned a bronze medal in the Junior European Championships in Keszthely. A year later, he was admitted into INSEP, a state institution for high-performance athletes. That same year, he earned the gold medal both in the individual and team event of the Junior World Championships in Antalya. During his first season as a senior, he won the Lisbon Grand Prix and the Paris World Cup, and earned a bronze medal in the World Championships in Havana. He finished the season No.4 in world rankings. After a dry spell in 2003–04, he won the Heidenheim Grand Prix and the Puerto Rico World Cup in 2005. The same year, he joined the French national épée team, which had won the Olympic gold at Athens. With Érik Boisse, Jérôme Jeannet and Fabrice Jeannet, Robeiri won the gold medal at the World Championships. The team would come to be known as “the Invincibles”, as they dominated men's épée from 2004 to 2010 with eight consecutive world titles. In the 2013–14 season, Robeiri placed second in the Berne Grand Prix and made it to the quarter-finals in the European Championships in Strasbourg before being defeated by Hungary's András Rédli, who eventually won the competition. A month after, Robeiri made it to the semi-final where he defeated his old teammate Gauthier Grumier. In the final, he prevailed over Park Kyoung-doo of South Korea to win his first individual World title. Robeiri graduated from the Polytech'Paris-UPMCengineering school. He works as an engineer within the information and communications systems division of RATP Group, the public transport operator for Paris, with a special contract which allows him to train and to attend major competitions.