3 years to French citizenship or a 10 year residency permit.
Best of all you need no work permit.You do however need to get to a recruiting office and they are only in france so.................
http://www.info-france-usa.org/atoz/legion/misc.asp
you also recieve french language emersion training!

http://www.legion-recrute.com/en/
Here is something I have not noticed before , the legion is looking for nurses.
also notice that a "private" who is overseas gets close to 4000 euros a month!
you have to have I would think a return airline ticket and perhaps a tourist visa
I have survayed the websites of commonwealth nations and a few will on occassion let a landed immigrant enlist many offer a shortened path to citizenship if you do so.
the USA will shorten the path to citizenship to a green card holder who enlists.
anyone else know of nations that go as far as france does in letting a no work permit non citizen enlisting?