I very much like the idea of a "2nd class" branch of the Royal Navy, a unit filled with socially undesirable people, treated with contempt by the rest of the Royal Navy. A group who are prepared to risk their lives to fight for their country and their honour, and gain respect from those who despise them.
So, take a look at this: Les Enfants Perdus. It's a similar concept, using soldiers from a social underclass as cannon fodder with grit and determination.
The problem isn't so much that the King would be unwilling to have foreiners fighting for him, the problem is that until very recently, Gallia has been completely isolated from the rest of Sirus. There are, quite simply, no foreigners within Gallia with which to form a foreign legion. Any foreigners arriving since the reunion are considered criminals and are hunted down. So, while I like the basic idea, a "foreign" legion really doesn't fit into Discovery lore.