I mean that's one of the benefits of being accepted into the FFL is that they literally give you a new identity and new life as a French citizen post-service, and during service they hold onto any documents you bring with. It's part of why France is so strict about the ''foreign" part. I've considered going and applying myself when I hit my 30s. The catch is that only 1 in 8 guys will make it in, and some of that is sheer luck. That's official stats but from what I understand it's more like 1 in 20. They more or less go over every aspect of your former military experience a requirement if you aren't from Africa or Eastern Europe
, personality, personal injuries, etc. They discriminate based on age (they like guys in late 20s/early 30s), sex (males-only), and criminal history. Certain types of violent crime and "smart" crime like tax evasion are seen as good criteria to have while usually the first question out of their mouth will be "why the fuck are you here?" if you have no criminal record. The only three crimes (outside of international crimes) that are red flags are rape, murder, and drug trafficking. If you meet all qualifications but aren't lucky, they'll tell you to try again in a few years. If they decide you won't make the cut during this extensive interrogation (that sometimes takes place through the course of your PT over several weeks), then they give you a paper more or less saying "don't try to come back under a different identity." They keep picture records on file for I think 5 years, so anon really only has two shots to get in. The FFL more or less acts as a policing unit in South America and North Africa that tends to have very high casualty rates due to being sent on the most reckless missions. Go figure since they aren't French nationals (yet). They get deployed elsewhere, but the French military doesn't like them being deployed to "French" and NATO skirmishes since that implies the regular military aren't doing their job.
I did a little reading just now out of curiosity and apparently you now need a "certificate of good behavior" to acquire French citizenship as of 2010 or so. That was never the case in the past, and is entirely reliant on your commanding officer granting it. Apparently the FFL has been seeing a rapid decline in applicants because of Chink Flu and that stupid certificate, since the officers use it like a whip against melanin-enriched legionnaires.