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Carlos Alcaraz battled from the brink to outlast top seed Jannik Sinner 4-6 6-7(4) 6-4 7-6(3) 7-6(10-2).
The 21-year-old became the first American to capture the singles title in Paris since Serena Williams in 2015.
Rohan Bopanna and his Czech partner Adam Pavlasek lost 2-6 6-7(5) to second seeds Harri Heliovaara and Henry Patten.
The 21-year-old also became the seventh man and the youngest to capture Grand Slam titles on all three surfaces.
The World No 1 defeated the Italian 6-2, 6-1.
Carlos Alcaraz reached his maiden French Open final with a 2-6 6-3 3-6 6-4 6-3 win over Jannik Sinner before Alexander Zverev also recovered from a slow start on Friday to beat Casper Ruud.
Swiatek defeated Coco Gauff 6-2, 6-4 while Paolini downed Andreeva 6-3, 6-1.
The second seed Indo-Australian pair lost 5-7, 6-2, 2-6.
They beat last year's finalists Sander Gille and Joran Vliegen in three sets.
Russian 17-year-old Mirra Andreeva sent second seed Aryna Sabalenka home, while Italian Jasmine Paolini staved off a fightback from fourth seed Elena Rybakina.
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