Charles-Albert Vuille was born on March 4, 1866 to modest parents in La Sagne. Vuille showed great promise and interned in Glasgow in 1886 before returning home to work. He spent the rest of his life in La Chaux-de-Fonds.
In 1898, Fabriques de Spiraux Réunies selected the 32 year old Vuille to manage day-to-day operations of the balance spring cartel, which was founded just three years earlier. He remained director of the company until it became part of ASUAG in 1931, at which point Vuille retired. He had befriended Charles-Edouard Guillaume, whose invention of Invar and Elinvar revolutionized the spring and balance industry.
Vuille was in charge of the Fabrique Suisse de Balanciers à La Sagne and oversaw the merger of that company with others to form the Société des Fabricants de Balanciers in 1907. He was president of that organization from the start, working alongside former competitors like Samuel Jaquet, Jämes Brugger, Edouard Vaucher-Zimmermann, and Charles Perrin.
In 1909 he was a founder of the electro-metallurgy company called Méteor, along with Jules Grumbach and Charles-Léon Schmid. But this company was not successful, leaving Vuille to oversee its liquidation in 1913 along with Jules Bloch.
When Emile Schweingruber's upstart balance spring factory in Saint-Imier fell on hard times, Charles-Albert Vuille moved in to take it over in the name of FSR. Along with Louis Huguenin of FSR and Schweingruber himself, Vuille oversaw the merger of this former competitor into the FSR in 1914 as the Fabrique de Spiraux de St-Imier.
He was also managing director of l'Usine des Reçues.
Vuille was called "intelligent, of an active and energetic temperament, experienced in all the finer points of business, a first-class administrator and a relentless worker, endowed with exceptional tenacity and patience" in his obituary. His tenure in charge of FSR and other organizations was long and prosperous.
He was one of the founding members of UBAH (Union des Branches Annexes de l'Horlogerie) and took over the presidency from César Schild, which he also held until his 1931 retirement. He was also one of the founders and an active supporter of the Laboratoire Suisse de Recherches Horlogères in Neuchâtel and for many years was a member of the Commission Cantonale de l'Observatoire.
Vuille died at 83 years old on May 25, 1949. He was already quite sick for some time and did not long outlive his wife, who died on March 6. She had long been a partner and collaborator of his, assisting with many of his activities.