Gaston Louis Christopher Borch was born on 8 March 1871 in Guînes, Pas de Calais, France, to a French woman (Emma Louise Sophie Hennequin) and a Norwegian father (Christopher Wolner Borch). Mlle Hennequin was an excellent pianist and soprano, and reportedly was once engaged to be married to the composer Jules Massenet. It is known that she performed a concert in collaboration with Massenet in 1860, and corresponded with him until her death.
Gaston Borch played the cello, and studied composition with Jules Massenet in France, Bruno Liljefors at the Valands School of Fine Arts in Sweden, and with Svendsen in Copenhagen. From 1893 to 1899 he conducted various orchestras in Norway. In 1898, his opera Silvio was presented at Christiana. At this point, he may have had private lessons with Grieg, who recommended him as "one of the best chefs d'orchestra, and most promising composers of our time."