He was born in Leeds on 21 March 1810, into a family originating in Hubberholme, Upper Wharfedale where his father, William Falshaw, attended the parish church in the morning and the Methodist chapel in the evening. James became an engineering apprentice, showing great skill with the theory and construction of skew arches which were not then generally understood. From 1831 he became one of the pioneers of railway construction in England. His first project was with the Leeds and Selby Railway and he was subsequently involved (as either construction engineer or director) with seventeen railway construction projects, at times being in charge of 8,000 men. His diverse skills were also applied to waterworks and reservoirs.
In 1838 he moved to Scotland, where he supervised the construction of the Highland Railway and the Scottish Central Railway and finally became Chairman of the Board of the North British Railway Company.
He lived in Edinburgh from 1858, becoming a town councillor in 1861 (having been nominated by Sir James Young Simpson), Baillie in 1864 and Lord Provost 1874-1877, the first Englishman and the first Methodist to hold that office. He managed the widening of Princes Street (to make it 'the finest street in Europe'), arranged for the purchase of the large private open space under the Castle to give it to the City as West Princes Street Gardens, and for the purchase of the Edinburgh Arboretum which became the Royal Botanic Gardens. He also improved the City's water supply and sanitation. His love of Edinburgh was also seen in his financing a stained glass window for St Giles Cathedral during the Chambers Restoration of 1872-1883.
He was Circuit Steward and a Class Leader at Nicolson Square WM. Whilst Lord Provost he hosted the visit of the (Methodist) U.S President, Ulysses S. Grant, and his wife at his home; Grant was made a Freeman of the City of Edinburgh and the Grants worshipped with the Falshaws at Nicolson Square. In 1873 he was appointed an official of the Relief and Extension Fund for Methodism in Scotland, and was one of the four Scottish representatives to the first Wesleyan Conference Representative Session in 1878.
His Christian philanthropic leanings resulted in his becoming Chairman of the [Edinburgh] Metropolitan Association for the Erection of Houses for the Working Class. His heraldic motto was In Officio Impavidus ('Fearless in duty').
He died in Edinburgh on 14 June 1889 and was buried in Dean Cemetery, where there is an impressive marble monument.