Nice to have news from France! I grew on clay in the Lot et Garonne, boulbene in fact, and no dig suits it well, such horrible soil to hoe and cultivate.
Six inches is a thick layer and too much to put over garlic cloves and bean seeds so they will be better planted into it, or plant them just in shallow holes in the existing soil surface, then cover with just two or three inches of manure.
I wonder whether you need the cardboard on top. The manure should cover all existing weed growth and as it is well rotted there will be little leaching of nutrients. Leaving it exposed to weather will speed breakdown of surface lumps and give a reasonable tilth by spring, especially if you use a rake or manure fork to knock it around a little on any fine days in late winter.
