Look there:
http://www.legion-etrangere.info/spi...?id_rubrique=8
Site in French, sadly, that's going to be the case for many vet sites like this one.
They ask not to download the songs, but you can just as well, or stream them directly. Open the link for each song, the download link is at the bottom of the page (after the lyrics!), select "Chant complet", click directly or save target on disk.
You can also find only some of these on
the offcial defense website, in section "Les chants trypiques de la Légion étrangère" (scroll down), in .rm format. Fewer available, but they sound somewhat better on the whole.
Else google the web for veteran sites of any Legion unit you can get the name of, that may get you some more useful links.
Hope you'll find what you were looking for!