When Mr. Willis pulls down Leeloo from the ceiling ventilation shaft/hole, he puts a grand piano underneath the hole so he can reach her. Watch when he puts the grand piano in place. It is pretty amusing how he just flings it there as though it were made out of cardboard.
Then again, maybe our ubiquitous action hero is very very VERY strong...
You have to conceive that fact that thi movie supposedly takes place in the future and perhaps that pianos in the future could be as light as...well, cardboard as you so clearly put.