Then at this point, it's beyond me. Like I said, I'm not the expert. What I can say is that what I've heard from those that do know is that inapte définitif is a pretty solid rejection. I believe this has been discussed before here at length, too. Lemme do some digging, and I'll get back to you on the matter.
Well, I can tell you that I know of someone (and no, I'm not one of these guys who knows someone who can only do one pull-up and only level 2 on Luc-Léger, but still manage to get ! They're sensationalists) who got inapte définitif and wrote a letter to the general commanding the Legion. He is currently serving.
How do I know, because Erika translated the letter he was going to write when we were in Mali into French.
Dan if you ever want to give it another go, send a letter to the COMLE asking for another chance. It obviously will not reach the general, but it will be taken into consideration by the appropriate office.
So it's possible, but super unlikely, and you need to write a letter to the COMLE to even have a remote chance.
Also, this topic has been discussed over and again on here. That particular dead horse has been kicked so much it's glue now. The search button is your friend.
You are not likely to get definitive for minor things. It is usually for a very good reason. The person that I was referring to in the quote Crawdad cited was someone who went rouge and then for reasons that I won't go into decided to leave. After getting his problems sorted he decided to try again. He wrote to the general (in French).*
He got accepted and was taken on. He made it to the end of basic training and asked to go civvy.
* It doesn't necessarily have to be in French, because there will be someone who will translate it. The fact that you are addressing the letter to the COMLE, is out of politeness, he won't even see it.
Définitif, means what it means : it's “thanks, but no thanks... Go find yourself another job.” You can appeal the decision by writing a letter to the COMLE. Some try, very few succeed. Then, you've got the unofficial work around... Try again anyway, after leaving enough time after being rejected, with or without a “different identity”, and hope that something will fall through the cracks and they won't spot you. I can imagine that some have already tried, I don't know if anybody has ever succeeded. Not exactly the same situation, but I was looking the other day a new documentary about the Legion selection process, where one could see a Russian guy trying to re-enlist under a new Id (using his mother's name), after having previously deserted. He was spotted and kicked out the selection process.