Train Hard - Stay Humble
...or descente, as they say in France.
6 years ago I saw this "move" in an old 90's clip of David, and now (this is from a 2009 Remington commercial) it still impresses me.
Also I don't see anybody doing this like that.
So that's what it's called! No, I don't think I've seen anyone do it like David Belle. He's so good he makes everything look so easy.
David is doing the same movement pattern as a lazy vault; this the same as a sequence that is often practiced in quadrupedal warmups at Sundays Basic sessions: forward QM->one foot to the side->other foot to front->feet together->push up from table position->balanced over two feet.
The music video is slightly different, though- more of a thief vault in that the outside foot (ie left hand, right foot) rather than inside foot leads off the ledge. Like lazy v. thief, though, they are only slightly different and their use will depend on a number of factors including approach speed to the ledge, footwork and personal preference.