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)
: 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.