Thank you Robert.
I fair bit of hoogle and translate later, I beleive that I am going to need another “cut-off” device in the new tableau. It will be on the floor below, 3m lower than the ENEDIS board and 12m further along the wall. If I have understood what I have read, a tetrapolaire “interrupteur sectioneur” should suffice.
The new board is already quite full, it is a Kegrand Plexos that can be connected to another tableau. I am thinking of adding another one with an interrupteur sectioneur and the parafoudre. From what I have read the latter is mandatory for any electrical installation where any part of the supply is above ground. ENEDIS ran the cables direct from their pole to the side of the barn, so it seems I must add one.
The same pole feeds the house the same way. There is, however, no parafoudre in the house.