I don't see the point in occupying this little square with a wooden structure while there are plenty of churches in Paris to host as many faithfuls as expected and that it would remove a touristic spot generating money.

By letting this parvis (square) free of a structure it should permits the visitors of the construction site to be able to watch it closer...

then, I see the swarms of the ironers, already jockeying for the contract. I think it would be a big mistake to not redoo it medieval style, using real wood. First wood is a living material, secondly after the restoration it would be possible with wood to open this area to the public, increasing the touristic value of the site. 

And it's a big support to the carpeting industries of France, yes, wood grown on and off the soil of France, only.

Finally, I am quite shocked to see the UNESCO trying to take hold and power over this utmost french site. What do they want? I guess we have to revert to the analysis of @mepatriot and the quests those "institutions" do to impose by all avenues their aims of becoming the one world gov.

No Kings of France would have allowed such an affront toward the sovereignty and independence of France without at least providing an astute necessary retreat after having attempted to handle the situation, even using violence :).

So no to the wooden temporary building, no to the "state of the art steel", and no to the UNESCO... go macron!