It was another early Grand Slam exit for Tsitsipas, who lost in the 2021 final to Novak Djokovic in an epic five-setter.
The 26-year-old has now failed to make it past the second round in his past four appearances at a major, while it is his earliest defeat at Roland Garros since 2018.
The defeat means Tsitsipas is set to drop outside of the world’s top 20 for the first time since August 2018.
By claiming the biggest win of his career, Gigante – who is making his debut at the French Open after going through qualifying – is rewarded with a third-round meeting with American 13th seed Ben Shelton.
Elsewhere, American 12th seed Tommy Paul pulled off an impressive comeback after being two sets down to beat Hungary’s Marton Fucsovics 4-6 2-6 6-3 7-5 6-4.
Paul will face Russian 24th seed Karen Khachanov, who booked his place in round three with a 7-5 3-6 7-5 4-6 6-2 win against Austria’s Sebastian Ofner.
Meanwhile, Lorenzo Musetti, the Italian eighth seed, went through to the third round with a 6-4 6-0 6-4 win against Colombia’s Daniel Galan.
In the men’s doubles competition, Jacob Fearnley, who won his first French Open singles match on Monday, safely cruised into the second round alongside Canadian Gabriel Diallo with a 6-0 6-2 win over Nicolas Barrientos and Rithvik Bollipalli of Colombia and India respectively.
Briton Luke Johnson reached the second round of a Grand Slam for just the third time as he and his Dutch partner Sander Arends beat Brazilian-Chile pairing Marcelo Demoliner and Nicolas Jarry 3-6 6-3 7-6 (10-6).
