Brasme made his international debut in February 2012 at the junior level in Kranj . In September of the same year he started in Oberstdorf for the first time in the Alpine Ski Jumping Cup . In February 2013 Brasme started at the European Youth Olympic Winter Festival 2013 in Râșnov, Romania . In the individual competition he reached 29th place before he was ninth with the team in the team competition. After Brasme subsequently failed to win a point in the Alpine Cup , he started in the FIS Cup for the first time in September 2014 . In Einsiedeln he jumped into the points twice as 26th and 27th. A week later he made it into the points for the first time in the same place in the Alpine Cup.
On December 12, 2014, Brasme made his debut in the ski jumping Continental Cup as a member of the French B-team . Until the end of the year he was without any points. Then he came back to the Alpine Cup in January. In Seefeld in Tirol he celebrated his first podium in this series as second. At the Junior World Championships 2015 in Almaty he was 22nd in the individual jumping. After the Junior World Championships, he celebrated two second places at the Alpencup in Kranj. At the end of February 2015, he was used again in the Continental Cup in Titisee-Neustadt and in the third event, he was 28th for the first time, reaching the points. At the end of March, he won the silver medal behind Vincent Descombes Sevoie at the 2015 French Championships in Chaux-Neuve . In August Brasme took part in the qualification for the Ski Jumping Grand Prix in Courchevel , but failed on the 47th. On January 16, 2016, he won an Alpine Cup competition in Oberwiesenthal for the first time.
At the Junior World Championships in 2016 in Râșnov, Brasme finished 30th in the individual jumping only in midfield. In the two team competitions, he and his teammates finished tenth. In the summer he took part in Courchevel, Wisła , Hinterzarten and Einsiedeln in the qualifications for the Grand Prix, but failed again. There were also no top placements in the Continental Cup. Only in Engelberg in December did he make it back to the points. At the following Junior World Championships in 2017 in Park City , Brasme jumped to 17th place in the individual. Three weeks later, he took part in the qualification for the individual competition of the Nordic World Ski Championships 2017 in Finland's Lahti part, reaching as 38 a starting place on the normal hill. However, he finished the competition itself only last in 50th place. A day later he started with Léa Lemare , Lucile Morat and Vincent Descombes Sevoie in the mixed team competition and finished tenth.