Although this is a grammatically masculine adjective in French, it is given to girls as well as boys in Britain and the Netherlands. In America it is more exclusively masculine. It is not commonly used as a name in France itself.
This name was not particularly common in Western Europe during the Middle Ages. It became more popular in part due to the fame of Prince Eugene of Savoy (1663-1736), a French-born general who served the Austrian Empire. A notable bearer was the American playwright Eugene O'Neill (1888-1953).
Other notable bearers include Owain the Great, a 12th-century king of Gwynedd, and Owain Glyndwr, a 14th-century leader of the Welsh resistance to English rule.