It stands for freedom, in the three words of the French slogan for it (sorry I am not very good with French and forget the words). They mean something on the order of Brootherhood, Unity, Liberty. This is the same thing which is symbolized by any of the Statues of Liberty which you will find - in the torch she carries. You will notice as well that the Fleur de Lis does resemble a torch and expecialy the one that Liberty carries.
The reason, as you asked, is that the organization is named after the French Foreign Legion and the Fleur de Lis is the emblem of that organization so I borrowed it. Symbol recognition is a very important part of why a symbol is used, and that symbol is quite readily associable with the Legion.
I hope this brief reply has answered your questions, if not please ask for further clarification and I will try again.
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One other thing I wanted to mention is that this logo is by no means the final thing.. this is only the first stage of a proposal toward that end. Anyone with an idea can make a counter proposal and once we have discussed the matter sufficiently then some roughs can be made up and the thing voted on. For now we will proceed along the lines of discussion and just see where it takes us.
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Oh, and the reason the Fleur de Lis resembles the lily flower, as you mentioned, is because that is what it is. The words Fleur de Lis mean Lily of Florence. Lis is lily. So, yes, it is a lily. Of course as nearly anyone can tell you the lily flower is also associated with Christianity and is often used around Easter time. By using this symbol in my proposal I was not intending to indicate the preference of any religion nor the exclusion of any other. So if the symbol is offensive to anyone on that basis (or any other) please indicate this in your discussion here. We do not seek to be offensive to anyone, although someone will no doubt find offense in whatever we do... this is human nature and a product of the great variety thereof. I would not have it any other way, I celebrate variety and never want to see a world of conformity to uniformity.. it would be so mundane and it would be so boring, and in some ways it seems to be there is a trend in that direction which bothers me.
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As to the shadows, I am not going to do that at this time but surely once we have a rough draft which has been voted on and approved then shadows will be added by someone for the final version. I am hoping to see some other proposals as well in order that we can have a variety to choose from by the time it comes to a vote on which to adopt.
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OK, after some searching I found the three words of the motto I was looking for.. the one which the Fleur de Lis and also Liberty's Torch represent.
The French National Motto The motto of the French Republic is "Liberty, Equality, Fraternity" (Liberté, Equalité, Fraternité). The site I took that from is here:
http://www.languedoc-france.info/06141203_motto.htm