Not true at all. The primary tenant of the Legion is "to fight for France but never on French soil". That's why the hold posts in the ex-French sphere of influence. They are mostly expatriates but many foreigners also. French can join the Legion, but like numerous others they either do so under a pseudonym or as a citizen of another country such as an ex-French colony.
Retired US Navy
NRA Life Member -- NAHC Life Member
"Take, sink, burn, or destroy the enemy fleet": Lord St.Vincent's orders to Nelson off Toulon, 21 May 1798
Pretty much spells it out, huh?