How do you make a board this way? http://www.alkita.fr/?page_id=250

What kind of foam, inserts, glass, resin... ?

How?
templates, planers, sanders, epoxy, glass, regular old inserts or make your own,
bam, like that that's how!
Seriously, looks like it is shaped from a blank of foam like a surfboard.
The rest looks like normal, more or less.
I bet they ride well, but harder to make than a wakeboard/snowboard style TT, more thought and skill going into achieving the shape.

You think it's just regular surfboard foam? No stringer? Where can you buy inserts?

Thanks

inserts? Amazon, google, etc. Usually .50 each or so, through the mail.
6mm usually is plenty good enough, kind of standard for kiting footstrap kits
Sorry I said surfboard foam before, looking at the pictures from the website closer, it seems to be airex foam instead, more used in $$$boats and airplanes than surfboards.
It's a strong, high quality expensive foam. No need for a stringer I think!
You might find some in a boat yard that works on megayachts or serious racing sailboats.
I have never tried to use it.
Corecell, divinycell, surfboard foam, 3# EPS, maybe 2# eps could work. Usually easier to buy too.
I would guess these boards would need 18-24oz glass top and bottom, like a regular TT...

I would stick with the regular fins though instead of glass-ons, easier to change it up, travel etc.

Show the result if you make something like that, it would be cool!