Mollassonne comes from the verb mollassonner, which means to laze around or become sluggish and soft. It's a less common, more descriptive verb than simply saying "I'm lazy."
In the song, Barbara Pravi uses it to paint a picture of cozy, relaxed inactivity: "Dans mes coussins, je mollassonne" (In my cushions, I laze around). It perfectly captures the feeling of blissful idleness on a rainy day, making it an engaging and memorable word.
"La Fête" finds Barbara Pravi picking her own couch over anyone else's party. She sends her regrets and stays home to watch the weather instead: "Sur mes carreaux, j'vois la pluie valser" (On my windowpanes, I watch the rain waltz). Curled up with her cat and a blanket, she keeps landing on the same line each time the chorus turns around, "Le temps s'arrête" (Time stops) - a quiet, rainy night alone is the only celebration she's after.