Adams was born in Malta the son of Andrew Leith Adams F.R.S., F.G.S.,, an army surgeon, who became afterwards well known as a scientist, a fellow of the Royal Society, and a travel book author. Francis' mother, Bertha Jane Grundy, became a well-known novelist. Francis was educated at Shrewsbury School and from 1879 in Paris. He took up a teaching position as an assistant master at Ventnor on the Isle of Wight, for two years. He married Helen Uttley and they migrated to Australia during 1882 where he soon dedicated himself to writing. He joined the Social Democratic Federation in 1883.

In 1884 Adams published a volume of poems, Henry and Other Poems (London), his autobiographical novel, Leicester, an Autobiography' (1885); and in 1886 a collection of works entitled Australian Essays. During the time of his residence in Sydney he was regularly employed writing for numerous Australian publications, including The Bulletin.

Adams then went to Brisbane and published 'Poetical Works' (1886, Brisbane) which is a quarto volume of over 150 pages printed in double columns. His wife died and Francis remained in Brisbane until the early part of 1887. He then published a novel, Madeline Brown's Murderer, (1887, Sydney).

In 1888 Adams published his best known piece Songs of the Army of the Night, which created a sensation in Sydney going through three editions in London. After a short stay at Sydney Adams married again, returned to Brisbane, and remained there until about the end of 1889 writing leaders for the Brisbane Courier. He returned to England during 1889 and published two novels, John Webb's End, a Story of Bush Life (1891, London), and he published The Melbournians (1892). A volume of short stories, Australian Life, came out 1892 and 'The New Egypt' was released after his death in 1893. Other posthumous publications were 'Tiberius' (a drama) and 'A child of the Age' in 1894 and 'Essays in Modernity' in 1899

Adams' health was failing rapidly from an incurable lung-disease and he spent the winter of December 1892-February 1893 in Alexandria to finish his book attacking the British occupation of Egypt. During the summer of 1893 he lived at Margate, England.

During a fit of depression caused by his hopeless illness Adams died by his own hand at Margate. He was survived by his second wife, Edith (née Goldstone), who assisted his suicide but was not convicted of any crime. A self-professed 'Child of his Age', Adams combined in his life and work many distinctive features of both fin de siècle British culture and the Australian radical nationalism of the 1890s, including a strong sympathy with socialist and feminist movements.An important work later published with an introduction by W.M. Rossetti is Tiberius (1894), a striking drama in which a new view of the character of the Emperor is presented.

Adams' industrious nature can be seen through his large output of written work his short lifetime. He often wrote quickly and did little revision; his work is often met with little critical merit. Songs of the Army of the Night has been reprinted in many editions, but the reputation of these poems ascends from their engagement with social issues, rather than their value as pure poetry for Adams was deeply sympathetic towards downtrodden races and men. At a time when London Dock labourers worked for four-pence an hour he could not help but raise his voice, and the rhetoric of his At the West India Docks echoed throughout the world of labour. Some of his verses provoked resentment in Conservative circles; but Adams perceived, as few did in those times, the depth of poverty and misery of a large part of the British nation, in an age before the introduction of unemployment insurance and old-age pensions.