My personal favorite vault. you run straight to the object, and right before you get to the object you turn slightly away from the object,put hand(s) on object, punch(two foot hop) toward it and you will spin in the direction you previously turned while lifting your legs over the object and letting go with the hand farthest away from the landing point when you are directly over the object. finally keep turning until you are facing the direction you are going land and I usually prefer to roll here(it flows so well) or keep running.
Notes: hand placement doesn't matter but if you want you can place your hands with the fingers facing the opposite way you are going or place it regular...doesn't really matter both can look the same, just pick the most comfortable. Hope this makes sense and is accurate.... not sure about french name or if there even is one.