Dürr won both the women's singles and the women's doubles titles at the French Open in 1967. (She was the last Frenchwoman to win the coveted singles trophy until 2000, when Mary Pierce ended a 33-year drought.) It was the first of a record five consecutive women's doubles titles at the event for Dürr (the record has since been equalled by Martina Navratilova and Gigi Fernandez). She won the women's doubles title again in 1973. She also claimed the French Open mixed doubles title in 1968, 1971 and 1973.

In addition to the French Open titles, Dürr also won the women's doubles at the US Open in 1969 and 1972. She won the Wimbledon mixed doubles title in her only title there although appearing in 6 Ladies Doubles finals at Wimbledon 1965-1975 .

Dürr was an integral member of France's Federation Cup team in the 1960s and 1970s.

Over the course of her career, Dürr won 26 singles titles and 42 doubles titles. She was ranked the World No. 3 woman player in 1967, and was ranked in the world's top-10 a total of nine times between 1965 and 1976. Her titles were won using unorthodox grips and strokes, giving way to pinpoint accuracy. Dürr was also the first woman to travel the tennis circuit with her dog, named Topspin, who became a star by carrying Durr's racquet onto court.

Dürr received the WTA Tour's Honorary Membership Award in 1988 for her contributions to the founding, development and direction of women's professional tennis. In 1993, she was appointed the first Technical Director of Women's Tennis for the French Tennis Federation (FFT). She was the captain of the French Fed Cup team from 1993 to 1996 and the co-captain of the team with Yannick Noah in 1997 when they won the competition. She retired from the FFT in February 2002.

In 2003, Dürr was inducted into the International Tennis Hall of Fame. In 2005, she received the International Tennis Federation/International Tennis Hall of Fame Fed Cup Award of Excellence.