He was the youngest of five children born to the carpenter, Henri-Louis Bocion (1792-1835), who was originally from Bournens, and his wife Suzanne-Catherine.
After his father's death, the family's financial situation became untenable and he was placed with his paternal grandfather, a marble sculptor, in Montreux.
His grandfather, in turn, died in 1840 and François went to live with his mother's family in Vevey, where he completed his primary education.
This inspired him to visit Paris in 1846, where he frequented the studios of Louis-Aimé Grosclaude and Charles Gleyre at the École des Beaux-arts.
From 1849 until his death, he was a Professor of Drawing at the École industrielle de Lausanne and designed the school's student uniform.