this was removed:
" belonging to France]]
It has a big natural resource in fish due to be a continental shelf larger than Greenland size. Estimates of biomass and abundance were produced for
eight commercial species. The total biomass was 245 000 tonnes and Patagonian toothfish
(Dissostichus eleginoides) accounted for half of the value (124 000 tonnes). The fish biomass
was distributed between the shelf and the deep sea. However, this evaluation remains
incomplete.http://www.ccamlr.org/ccamlr_science/Vol-16-2009/01Duhamel-Hautecoeur.pdf

The continental shelf teem with life, because of the sunlight available in shallow waters, in contrast to the biotic desert of the oceans' abyssal plain. The pelagic (water column) environment of the continental shelf constitutes the neritic zone, and the benthic (sea floor) province of the shelf is the sublittoral zone.Pinet 316-17, 418-19.
Most commercial exploitation from the sea, such as metallic-ore, non-metallic ore, and hydrocarbon extraction, takes place on the continental shelf. Sovereign rights over their continental shelves up to a depth of 200 metres or to a distance where the depth of waters admitted of resource exploitation were claimed by the marine nations that signed the Convention on the Continental Shelf drawn up by the UN's International Law Commission in 1958. This was partly superseded by the 1982 United Nations Convention on the Law of the Sea.http://untreaty.un.org/ilc/texts/instruments/english/conventions/8_1_1958_continental_shelf.pdf which created the 200 nautical mile exclusive economic zone and extended continental shelf rights for states with physical continental shelves that extend beyond that distance.

France extend its jurisdiction over 567 732 square kilometers of the neighboring continental shelf from the land area of 7 215 resulting in 574 947 square kilometers. There are besides some fishing boats and vessels, owned by fishermen on Réunion Island, a department of France approximately 3,300 km (2,100 miles) to the north, who are licensed to fish within the archipelago's Exclusive Economic Zone.

Govern of France principal activities on the Kerguelen Islands focus mostly on scientific research, earth sciences and biology. 
The so-called Kerguelen microcontinent or Kerguelen Plateau include charcoal and conglomerate fragments of gneiss indicate that much of the plateau was above sea level an covered by dense conifer forest.  Tt sanks 20 million years ago and is now  below sea level. It has sedimentary rocks similar to the ones found in Australia and India, suggesting it was gondwanan origen.

The former sounding rocket range to the east of Port-aux-Français  is currently the site of a SuperDARN radar.

Since 1992, the French Centre National d'Études Spatiales (CNES) has operated a satellite and rocket tracking station which is located four kilometers east of Port-aux-Français. There was a need for a tracking station in the Southern Hemisphere, and the French government required that it be located on French territory, rather than in a populated, foreign place like Australia or New Zealand."

In the photo you can see that the continental shelf is big. The economic importance is referenced. But Nadietalent reverted too, another page related with a flooded laurel forest in Ghana with economic value. I prefer not do a War with a person.