The funny thing is that Naturpapier is in fact "uncoated paper."
So what you have is an oxymoron, i.e., "specially coated, uncoated paper."
So what are we to do? Let's just pretend that since the paper is now coated we can no longer refer to it as uncoated. Thus: specially coated paper.
Info comes from my International Glossary of Technical Terms for the Pulp and Paper Industry.

Spezialbeschichtetes Naturpapier is a contradiction in terms. The unique feature of Naturpapier is that it is uncoated. From a (recommmandable) paper glossary:

Allgemeine Bezeichnung für holzfreie oder holz-
haltige Papiere, die im Gegensatz zu gestriche-
nen Papieren keine Veredelung durch einen
Strichauftrag haben. Sie können auch als unge-
strichene Papiere bezeichnet werden.
(http://www.grafedruck.com/pages/PDF/plexikon.pdf, page 33)

Here's what the manufacturer has to say about the Fly paper:
FLY.DESIGN.PAPIER mit 1,2fachem Volumen und spezial geglätteter Oberfläche ist das leistungsstärkste Sortiment im Bereich Naturpapiere.
http://www.papierunion.de/page=presse__artikel/id=24074.jsp

So it's specially calandered, not specially coated. Usually, this is referred to as supercalendered or SC:

Paper: After 30 Years, Part II - [ Diese Seite übersetzen ]
... US is supercalendered, uncoated groundwood paper for Sunday magazine sections. Its
US consumption is expected to reach one million tons by 1987. Uncoated Paper. ...
www.stanford.edu/dept/SUL/waiscool/andl/an11-720.html

Fact Sheet - Recovery and Recycling of Paper and Board - [ Diese Seite übersetzen ]
... Laid is an uncoated paper or board with closely spaced horizontal watermark lines
and ... It is not as glossy as supercalendered paper and is used for booklets and ...
www.paper.org.uk/info/factsheets/descriptions.htm