This 1965 short film by Jim Henson is titled Run Run, and is more like a glimpse into his life through some edited home movie footage. There are no puppets or Big Birds, just his children gleefully running through the Connecticut woods, crunching leaves with their feet, and in the end (spoiler!) finding their mom, the late Jane Henson.
Some background on the footage (which includes credits and everything) can be found at Jim Henson's Red Book:
"Family art projects were the norm, and Jim painted large oil canvases depicting the colored light that filtered through their wooded yard. One personal project inspired by his family and their forested surroundings was Jim’s short film, Run Run. Trying to integrate movement, music and light, Jim filmed his young daughters joyfully running through the woods behind their house. The changing colors, shadowed and lit by the sunlight, move to the musical score, a gentle piece composed by Joe Raposo, and the girls travel among the trees and out into a clearing. Their mother, wearing a red dress reflective of the autumn leaves, meets them and leads them home.
While Jim did not use Run Run commercially, it gave him some experience meshing filmed images with music tracks to evoke an emotional response."