Nope, this specifically refers to the French concept of Foreign Legion, a non-conscripted army fighting exclusively out of France. What you describe is simply the modern professional standing army. It wouldn't make sense for those to have a bonus for fighting abroad, it should be the opposite: a bonus when fighting in defense of the state/homeland (as opposed to fighting for a monarch).
The "Volunteer Army" refers to what Louis Philippe introduced during the Monarchie de Juillet and that endured during the following Republic, the Second Empire, the Republic again.. Potentially dangerous elements for the state, as they could become militia for someone planning a coup d'état (ex-mercenaries who had served the last Bourbon king, mostly Swiss, ex-revolutionaries who were often political refugees in Republican France from Russia, Prussia, Austria etc. and Frenchmen as well) were offered jobs as soldiers for France. Those units, with special training, to develop their esprit de corps, were to be kept outside France (that's the whole idea...) - on the offensive/defense in its colonies in Africa, mostly. The concept was copied elsewhere afterward.
I agree it's a somewhat way too specific concept and it should be replaced with "professional/non-conscript" army and another unit than the Foreign Legion, but the thing is they made a tenet for Freedom from the old French UU and the concept behind it, taking it as is. It's still fits for Freedom as this was an early idea to secure a fledging constitutional regime by removing ex-soldiers and potential fighters that seditious political elements (either pro-Bourbons, pro-Bonaparte or anti-Orléans) could use to topple the constitutional government.
I realize I'm not supposed to say this on the interwebs, but I did not actually know a lot of this, or about the Legion's history in general. Thanks for this. I briefly looked up the details you cite and you are indeed correct.
I nonetheless still don't understand the point you're making. Per wikipedia, and yourself, the Foreign Legion was set up by an autocrat, NOT a democracy. When you correctly point out that "seditious elements" could have exploited the human resources of the Legion Etrangére, you omit that those elements would have been seeking to replace the last King of the French by a republican form of government. Unless you are claiming King Louis Philippe as a representative of the Freedom ideology because of his constitutionalism, I really don't follow your argument. If anything, it backs up my point that Autocracy - which I realize refers more to fascism than monarchy - should have the Volunteer Army tenet.
Furthermore - and on this I may well simply be uninformed - I cannot find a single source using the term "volunteer army" in the context you mention, i.e. either specifically to the Legion or to the concept of a unit made up entirely of foreign volunteers. I can however find numerous references to "volunteer army" or "volunteer military" with reference to the contexts I refer to, i.e. as a non-conscript army raised by liberal democracies as a substitute for conscription specifically because it is anti-democratic.
http://en.wikipedia.org/wiki/Volunteer_military
http://www.rand.org/pubs/research_briefs/RB9195/index1.html
http://www.shsu.edu/~his_ncp/VolArm.html