Antoine
That parrel setup looks pretty similar to my standard Sunbird rig, with the minor exceptions:
On mine, the upper luff hauling parrel from second to third batten from top goes around the mast the other way - same as the lower two.
The bottom of the lower luff hauling parrel goes from the lowest batten direct to a block on the deck - yours goes around the mast again before doing that. Seems to me that will add friction without any noticeable gain in sail control.
Having said that, you don't appear to have a fixed parrel on the lowest batten - mine does - so perhaps this extra loop is intended to perform that function? I think I would remove it, and put a fixed parrel on that batten.
Chris