I am currently working with a Corsican and this is something we regularly discuss.

In fact, it's incorrect to assume that there is little activity. Even today, in the 2000's, Corsica has a death rate about 9 times higher than mainland France. In a nation of 250, 000 a clan feud murder takes place every month or so.
For the (attempted) hit this year with the most publicity in France, see below:

http://www.english.rfi.fr/france/20120528-godfather-style-shooting-corsica-hospital

The Corsicans of course are not a huge international syndicate, but in their island and region of Europe, a very strong group, with interests in the usual areas. Especially they profit from tourism in the south of France, with lots of investments in casinos, hotels, beach restaurants (it really seems like every Corsican owns a restaurant!).
On the island itself, a lot of people who are not necessarily organized crime members are somewhat involved in semi-underground deals. The friend of which I spoke, for example, was selling contraband cigarettes in his shop.

But hopefully there is someone who has better infomation than just anecdotal information.