The fourth division club fought valiantly until Turkey striker Mevlut Erding finally broke the deadlock in the 53rd minute by heading home the winner.
PSG, who have lifted the Cup seven times, will face Monaco in the final. The principality team advanced by beating Racing Lens 1-0 after extra time on Tuesday.
"I guess PSG deserved to win because they are a lot more powerful than we are," Quevilly coach Regis Brouard told reporters.
"I wish to congratulate my players for what they have accomplished. I'm really proud of them."
His PSG counterpart Antoine Kombouare paid tribute to the amateurs from Normandy, saying: "We knew we had to respect Quevilly and they showed why tonight by giving us a hard time.
Some 800 police were on duty. No incidents were reported around or during the game, attended by a 21,000 partisan crowd, roughly the Quevilly population, clad in yellow and black, the club's colours.
