Providing the aperitif, Cornet, who made her French Open debut as a 15-year-old in 2005, will need to draw on all her experience to see off Czech 20th seed Barbora Strycova.
Up third, Monfils may relish a return to a more traditional brand of tennis against 95th-ranked Brazilian Thiago Monteiro, having stretched the sport's parameters in the first round in a trick shot-laden straight sets win over Germany's Dustin Brown.
Sandwiched in between, third seed and 2015 champion Stan Wawrinka will hope to extend a good run on clay, and iron out a statistical quirk, against Ukraine's Alexandr Dolgopolov.
Wawrinka has never lost to a player ranked outside the top 50 at the French Open but 89th-ranked Dolgopolov has won twice and lost just once against the Swiss, and claimed the third tour title of his career in Buenos Aires in February on clay.
(Reporting by John Stonestreet; Editing by John O'Brien)
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