Meillard comes from the canton of Neuchâtel and learned to ski at the age of two. When he was 14 years old, he and his family moved to the canton of Valais . In November 2011, at the age of 15, he started taking part in FIS races . At the end of the next season, he celebrated his first victory in an FIS race (in the Super-G discipline ) in April 2013 , where he left World Cup winner Sandro Viletta behind. He made his debut in the European Cup on January 11, 2014. Two weeks later, he surprised everyone with a fourth place in the European Cup combined race in Crans-Montana , the youngest of all participants.
In the 2014/15 season, Meillard established himself as the world's best giant slalom racer of his year. He made his first appearance in the World Cup on January 10, 2015 at the giant slalom in Adelboden , where he finished 51st. On January 28th, he won his first European Cup race, a giant slalom in Crans-Montana. With two further podium places, he classified himself in third place in the discipline classification. He also won the Swiss Slalom Junior Championship. In March 2015 he won three medals at the Junior World Championships in Hafjell : gold in the super combined, silver in the giant slalom and bronze in the super-G. He finished the season with the Swiss championship title in alpine combined.
Due to his performance in the European Cup, Meillard secured a fixed starting place for the following 2015/16 World Cup season . This was initially very difficult: In the first seven World Cup giant slalom he was unable to qualify for the second round. On February 28, 2016, he broke through this negative series and got his first World Cup points with 27th place in Hintertoder. Six days later, on March 5th, he advanced to the top of the world and surprised everyone with 8th place in Kranjska Gora .
While the 2016/17 World Cup season started rather cautiously, Meillard celebrated his fourth victory in a European Cup race on December 14, 2016. Four days later he was unable to compete in the second run of the World Cup giant slalom in Alta Badia . The reason was a meniscus damage on the right knee, which required an operation. He then had to take a break for about a month. Shortly before the end of the season, he won the gold medal in giant slalom and combined at the 2017 Junior World Championships in Åre .
On December 19, 2018, Meillard achieved the first World Cup podium finish with second place in the giant slalom in Saalbach-Hinterglemm . A day later followed with another second place, the first podium in a slalom. He achieved his first World Cup victory on February 9, 2020 at the parallel giant slalom in Chamonix ; thus he also won the first parallel discipline ranking.