The Legion has always been the units for dirty wars and heavy secret ops for which the actual commandos were too light. Since they have light armor, artillery and engineers, I guess they would still be able to take over a small country all by themselves.
As loktarr said, the guys who sign in are generally fleeing, either criminals or overall reprobates who have no other choice than lifelong clandestinity or the Legion, which is lifelong clandestinity with traditions and someone shouting at you constantly.
They owe a lot to their unit, and since they are mostly foreigners they are about the only people in France to get a proper patriotic sense (however terrifying that will look to our American friends here), except for those who haven't reached hat level and stick along for the action, the occasionnal kill and the free beer.
They are the last chance for themselves, and used as the last chance in contingency, before it really turns awful.
And yes, they generally see more action than is known of, even action where people will not know there is action at all. But there are no conscripts anymore in France, so maybe the legal rule for engagement has been loosened a bit?
BTW, I guess there is a special downgraded rating for draftee units? That would be useful for dragging down the average in drafting countries, like Germany or Russia, where more or less of the force is conscription units, though there are some very good professional 'showcase' units which will be involved more easily and have the 'top standard' experience.