Having broken the lap record at the circuit in Friday's practice, Marquez went even faster early in the second qualifying session to set the tone for Q2.
Quartararo, however, managed to complete one more lap to clock 01:29.324 seconds as the home crowd erupted and sang "La Marseillaise", the country's national anthem, even as the Frenchman urged them to calm down.
"It was amazing to get this pole position, thanks to all the fans supporting us. It's a really important pole position but we need to get the points later and on Sunday," Quartararo said.
It also marked the first time since his championship-winning season in 2021 that he had clinched back-to-back pole positions having gone fastest at the Spanish Grand Prix.
"Fabio rode in an incredible way, he deserves this pole position in front of his fans. He was doing a superb job in Jerez (at the Spanish Grand Prix) too," Marquez said.
"But I'm happy with my pace and starting on the front row was my main target."
World championship leader Alex Marquez of Gresini Racing was third fastest and his teammate Fermin Aldeguer will start on the second row alongside KTM Tech3's Maverick Vinales and Ducati's Francesco Bagnaia.