Despite having Sardinian parents, Francesco Cossu was born in Roma where his family had moved to. He graduated in law and then worked in a bank. At the same time Cossu had a passion for rowing and joined the Circolo Aniene under coach Antonio Ghiardello. In 1931 Cossu was elevated to the coxed fours with Ghiardello as his stroke and, after winning the Italian Championship, the crew went to that year´s European Championships in Paris and dominated the final ahead of Denmark and Switzerland.
Cossu started the 1932 season on the eights, but Ghiardello moved himself and his three European gold-medal winners to the coxless fours, and they won the Italian title and Los Angeles Olympic trial. At Long Beach, they won a bronze medal. It was a disappointment, however, to finish third out of only five competing nations, particularly after winning their heat more than six seconds faster than the eventual gold medallists Great Britain achieved in their heat. Cossu retired shortly after the Los Angeles Olympics at just 25 years-of-age to concentrate on his work in Roma. He died in the Italian capital in November 1986, a few months before his 80th birthday.