At the beginning of the excellent documentary Warriors of the French Foreign Legion, French General Bernard Grail is asked why the legion excludes women. He responds by saying that, "For the moment it is impossible for us to accept women into the legion because our training system and our day to day life within the legion won't allow it. To make this family work and create a cohesive unit from this group of foreigners we have to place everyone in a big bowl, close the lid and shake it around."
General Grail's "soup-bowl" is a barracks and training ground where the recruits live together and train together. Legionnaire boot camp is notoriously brutal, the recruits are placed under extreme calorie restriction while being expected to perform mentally and physically. For weeks on end they undergo a constant regimen of forced marches, obstacle courses, and jogging while simultaneously having to learn the French language. After boot camp they go on to specialized infantry training, which is also extremely demanding. They train as they fight, in small groups far away from their bases in some of the most remote and inhospitable places on earth.
Most would not consider them to be an elite unit in the mold of our Army Rangers or Navy Seals. They accept men who would be rejected by other countries' militaries, most notably those with criminal records. The contemporary legion does reject some people with criminal backgrounds due to the nature of their offenses, but the standards are notably laxer than the U.S. military's. At any rate, many of the recruits appear to come from poor countries, perhaps motivated by the prospect of a job and a French passport.
Regardless of how elite they are, the Legion is unapologetically an instrument of state policy and not a vehicle for self-actualization. France created the Legion so they could interfere in faraway places without risking French lives. Former Legionnaire Tony Kadish described the attitude thusly, "...if things do work out, fine they can give the glory to the French Army. And if they don't, well so a few foreigners got killed, no big deal."
The documentary confers a profound respect for the bravery of these men, it also provides an appreciation for the value of single-sex institutions. The documentary describes an operation where they had to evacuate several thousand French Nationals scattered across West Africa, the amount of discipline, bravery, and cooperation needed to accomplish that is staggering. It's hard to imagine a mixed-gender unit being cohesive enough to work independently in the jungles of West Africa, while engaged in combat over a period of weeks. How would the male legionnaires react to women getting shot? Would the men cooperate with each other, or compete for female affections. Private firms spend an untold amount dealing with issues arising from a mixed-gender workforce. Clearly it is something that can be problematic. Where only money is at stake it might make sense for the law to place a priority on equal opportunity, but where human lives are at risk it doesn't. Human life should always be the top priority.