The 18-year-old Townsend is ranked 205th but earned a wild card from the U.S. Tennis Association based on her results during a series of lower-level tournaments this spring.
Now she’s the youngest U.S. woman in the third round at Roland Garros since 2003. Next is a match against No. 14 Carla Suarez Navarro of Spain.
Townsend won the girls singles and doubles titles at the 2012 Australian Open and became the first American since 1982 to hold the year-end No. 1 junior ranking.
Cornet, 24, had her best Grand Slam result at the 2009 Australian Open, getting to the fourth round.
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