But the Germany goalkeeper will have the chance to get back on track at Frankfurt, who he left for PSG in 2015.
"When I was in Paris, I always liked to recall the great time I had in Frankfurt," Trapp told the club's official website. "The Europa League season in 2013-2014 was special and of course I would like to experience it again.
"I was very happy for Eintracht in May, when they won the DFB-Pokal. For me, it was important to get into an environment in which I feel good and where I can play, I'm looking forward to another year at Eintracht."
PSG confirmed there is no option to buy clause included in the loan deal with Eintracht.
Eintracht Frankfurt sporting director Bruno Hubner said: "Frederik Ronnow's current knee problems have made us think, unfortunately our goalkeeper has suffered a knee injury in pre-season that has not quite healed and is still bothering him.
"We believe in his qualities but he has now given us the chance to sign Kevin - a goalkeeper who is not only ready to play, but also a figure with great leadership potential, and who demonstrates the value of our club. A current national player decides against other top clubs and comes to us."
Eintracht will find out their Europa League opponents on Friday, having been placed in pot three for the draw.