Baptiste Mischler comes from Haguenau. His parents were also active in athletics in their youth. When he was five years old, he and his older sister started athletics in Brumath .
Mischler has been competing in medium-distance competitions on a national level since 2013. In the summer he took part in the European Youth Olympic Festival in Utrecht and was victorious over the 1,500 meter distance in 3: 57.38 minutes. In 2014 he qualified in an elimination competition in Baku for the Youth Olympic Games in Nanjing, where he finished sixth over 1500 meters. In 2015, at the age of seventeen, he started at the U20 European Championships in Eskilstuna, Sweden, where he won the silver medal in 3: 49.88 minutes. He then passed his baccalaureate at the Heinrich Nesse School in Hagenau and then began studying topography at the Institut national des sciences appliquées de Strasbourg .
In 2016 he finished fourth over 1500 meters at the U20 World Championships in Bydgoszcz. A year later he was fifth at the same venue over the same distance at the U23 European Championships . In August 2017 he started at the Universiade in Taipei over the 800 meters, in which he narrowly failed in the semi-finals as third and finished 12th overall. In 2018, Mischler competed in an international championship race for the first time in an international championship race at the European Championships in Berlin. With 3: 50.96 min he failed in the run and finished 27th over the 1500 meters. Two months earlier he set a personal best that was more than ten seconds better than his lead time in Berlin. In July 2019 he last competed at the U23 European Championships . In Gävle he took fourth place over 1500 meters.