Friedrich Baume, later called Frederick Ehrenfried Baume, was born at Dunedin, New Zealand, on 13 June 1862, the son of Joseph Baume, a photographer, and his wife, Emilie Ehrenfried. He was educated at Thames and at the High School of Otago (later Otago Boys' High School) in Dunedin.
Baume was engaged in commerce and journalism from 1877 until 1883, and was admitted to the Dunedin Bar in 1884. He then enrolled as a student at the University of Otago and won prizes in mental science in 1885 and political economy in 1887. About 1888 he and his mother moved to Auckland, Joseph Baume having become an itinerant. Baume set up in legal practice with a retainer for licensing cases from Ehrenfried Brothers, the brewery firm founded by his uncles, Louis and Bernard Ehrenfried. He also enrolled at Auckland University College, and was prominent in student activities before graduating LLB in 1891. He retained a lifelong connection with the college, becoming an examiner in law, a member of the college's council from 1894 to 1910, and president of the Auckland Graduates' Association. He later pursued the college's interests in Parliament.
In 1896 Baume set up a legal practice with A. E. Whitaker, son of the former premier Sir Frederick Whitaker. He soon became prominent in many aspects of Auckland life: he was a member of the Auckland City Council and Auckland Harbour Board, a leader in the Auckland Jewish community, president of the Auckland Law Institute, president of the New Zealand Natives Association, and an active member of many other bodies. An ardent imperialist and devoted follower of Rudyard Kipling, he advocated compulsory military training and served as a captain in the New Zealand Native Rifle Volunteers. He also contributed to the cultural life of Auckland as an outstanding lecturer on literary subjects and as an accomplished actor.
In 1902 Baume was elected to Parliament for City of Auckland as a Liberal and in 1905 won the Auckland East seat. He was considered for membership of Joseph Ward's first cabinet in 1906, but his connections with the liquor trade saw him passed over in favour of George Fowlds. As minister of education, Fowlds had Baume removed from the chairmanship of the parliamentary Education Committee in order to limit his scope for causing political trouble. Baume later intrigued with Liberal country members to counter Fowlds's single-tax views. He believed that 'the groundwork of the whole life of this Dominion is the work of the farmer', and supported the conversion of leasehold to freehold titles.
As a brilliant university scholar and an eloquent speaker with wide leadership experience, Baume brought distinction to the deliberations of Parliament and contributed his services willingly for the welfare of the country. His services to the legal profession were recognised in 1907 when he was among the first group of New Zealanders to be appointed King's counsel. Baume also served as vice consul for Denmark from 1900. He was an ambitious and determined man of rigid convictions and a quick temper. In Parliament many believed he was destined for high office – perhaps as Speaker – but a decline in health caused his resignation in 1910. (A serious heart attack in 1909 had resulted in the premature announcement of his death.) He went to a mineral spa at Bad Nauheim, near Frankfurt, Germany, for treatment of his heart condition and died there on 14 May 1910.
In San Francisco on 21 June 1899 Baume had married Rosetta Lulah Leavy, a university graduate and one of the first women high school teachers in the United States. They had four sons: Frederick Ehrenfried (Eric), Neville, Alan and Sidney. Eric became prominent as a journalist, broadcaster and novelist in Australia. Rosetta Baume became the first woman candidate for Parliament in 1919. In 1921 she married E. W. Kane, clerk of the House of Representatives. She died in Wellington on 22 February 1934.