I think for former criminals who have finished serving their time, the Foreign Legion would be a chance for a fresh start if they chose to keep the new identity that the Foreign Legion assigns to them.
Also, HN-ers beware -- the FFL doesn't take people without military experience, anymore.
Source: am a reserve infantryman at 94th RI, 3rd Company. Regularly train with 2ème REP.
I would imagine US soldiers with blemished pasts would be candidates