Eddi Gutenkauf lived much of his life in Ettelbruck, but moved around to various clubs during his sporting career. He took up fencing in his youth and quickly came to specialize in the épée category, in which he won individual national championships in 1958, 1961, and 1963. In 1960, he was selected to represent Luxembourg in the épée at the Rome Olympics, where he was eliminated in round two of the individual competition. In the team tournament, he was eliminated in the quarterfinals alongside Roger Theisen, Edy Schmit, and Robert Schiel. He retired from active competition in the 1960s and settled into private life.