That Wiki link is rather devoid of information about the Marathon des Sables... I would know, as I ran it in 2009. I'm not sure how the Foreign Legion factors into the race, as it was started by Patrick Bauer in 1986(who still oversees it).
People of all ages and from all walks of life participate in it. It's a life changing event in which you learn so much about yourself and develop deep friendships with people you've only known for perhaps a few days at most. The participants also suffer.. a LOT-between heat, physical exertion / exhaustion, and being fully self-sufficient for a week. It's a damn grueling event that definitely earns it's spot among the world's toughest foot races.
I understand, regarding the legion. I'm sure there are a lot of military folk who ran it. I know of at least one US Marine who ran it. There were a number of Rugby players and French firemen who were the talk of the town that year, too!
Ugh, 54 hours. I got hurt at the end of the first day and had to walk... and got really sick during the long stage which forced me to take frequent rests during the remainder of that and the marathon stage. As for me, I'm from the United States and trained in New Jersey. Hardly the conditions of the Sahara, but you make it work :)
If you asked me right after the race, I would've said no. I was in so much pain.. but about a month later I felt like I had to again. If you can pay the high entry cost(~$4,000 USD), it's worth it. I'm going to try to go back in 2013.
The Foreign Legion's has it's own version, MDS, "Marathon des Sables" ~ http://en.wikipedia.org/wiki/Marathon_des_Sables