Current Family History

Probably a variant spelling of English Currant, from Old French courant, present participle of courir ‘to run’, which Dauzat and Morlet suggest is an ellipse for chien courant, and hence a nickname for a hunter. In some cases, the name may be an Americanized form of the French cognate Courant, for which Morlet also offers an additional source: a habitational name from any of various minor places named (Le) Courant, from courant ‘running’, in the sense of ‘running water’, ‘water course’, a derivative of kaour from Old Breton cobrand, from cobr ‘help’, ‘aid’.

Source: Dictionary of American Family Names ©2013, Oxford University Press