Francis Henry Samuel Orpen was the eldest son of Reverend Dr Charles Edward Herbert Orpen (MD), member of a family of Irish landed gentry, and his wife Alicia Francis Coane (born Sirr). Two of his younger brothers were Charles S. Orpen* and Joseph M. Orpen*. Francis studied medicine for three years but had to give up because of health problems. He came to the Cape in 1844 to recuperate, accompanied by his brother Charles, and remained in the Colony. During the next few years the rest of the family followed them to South Africa, where Charles senior financed his sons' farming venture on the farm Taai Bosch Fontein near De Aar. In 1849 Francis was admitted to practice as a land surveyor and three years later he and his brother Joseph were appointed as surveyors in the Orange River Sovereignty (now the Free State) under the superintending land surveyor of the territory, J.H. Ford*. When Britain gave up the Sovereignty in 1854 - a move which Francis strenuously opposed - he left the territory and later settled on the farm Sinclair along the Vaal River near present Douglas. On 23 October 1855 he married Sarah Anne Murray (1834-1906) with whom he had eleven children. Two of their daughters, Katherine* (Kate) and Lilian*, were active in natural history and archaeology, while Francis himself presented some marine molluscs from the Cape coast to the Albany Museum in Grahamstown.
In 1867 Francis and David Arnot, an agent for the Griquas, planned a settlement just north of the Orange River, near its confluence with the Vaal River, with Douglas as its seat of government. Francis surveyed the settlement and became civil commissioner and resident magistrate at Douglas. He and Arnot campaigned for the annexation of Griqualand West and its diamond fields by Britain, which took place in 1871. During that year Francis extended the coastal triangulation that Captain W. Bailey* had completed in 1863 some 100 km northwards to the Orange River, connecting it to a survey made by his brother Joseph in the Aliwal North division.
After the annexation of Griqualand West Francis was appointed magistrate and (in October 1872) surveyor-general of the territory. Also in 1872 he was instructed to survey the disputed border between Griqualand West and the Orange Free State. His recommendations and map showing the location of the border were accepted by both parties in 1876. Also in 1872, and again in 1874, he was appointed as a commissioner to report on conflicting land claims. As the Orange Free State continued to contest the rights of Waterboer to the diamond fields, the lieutenant-governor of Griqualand West, Sir Richard Southey*, asked David Arnot and Francis to substantiate Waterboer's claim. This they did in The land question of Griqualand West: an inquiry into the various claims of land in the territory, together with a brief history of the Griqua nation (Cape Town, 1875). Francis subsequently compiled a detailed map of Griqualand West on six sheets (1878).
When Griqualand West was incorporated into the Cape Colony in 1881 Francis retired on pension and was elected as a member of the Cape House of Assembly for Barkley West, one of the two constituencies into which the former territory was divided. He served the constituency for two years. During this period the (short-lived) South African Institution of Engineers, Architects and Surveyors - the first engineering society in southern Africa - was founded in Kimberley in October 1881 and Francis Orpen elected as its first president. He was furthermore a Fellow of both the Royal Astronomical Society and the Royal Geographical Society. Throughout his life in the Cape Colony he was engaged in scientific pursuits, particularly in astronomy and geology. When the astronomer Dr W.S Elkin* visited Kimberley in 1881 Francis provided him with astronomical instruments to make the first accurate determination of the longitude of the town.