The reference to most likely refers to the signing of divorce papers in the Friends episode "The One With Joey's Porsche" (Season 6, Episode 5).
Alternatively, if you are looking for a specific short film about "paper," you may be thinking of the Academy Award-winning Disney short , which features a man using paper airplanes to find "the one" (his soulmate). "Friends" The One with Joey's Porsche (TV Episode 1999) [S6E5] The One
: Ross and Rachel appear before a judge to seek an annulment, but because Rachel included false allegations (claiming Ross was mentally unstable and a drug addict) on the application, the judge rejects it. The reference to most likely refers to the
: Consequently, the two are forced to file for a legal divorce instead. They conclude the episode by signing the actual divorce papers, which marks the official end of their impulsive Las Vegas marriage. : Consequently, the two are forced to file
: During the signing, they share a poignant conversation about their shared past and how they both originally imagined that if they ever got married, it would be forever.