That should work fine, except for the plugins, since each plugin has its own locale file, and it will look for locale_mysite_en_UK in the locale folder of the plugin, not find it, and default to locale_en_UK, so that is okay for the UK version, but not for the fr_FR version.
Oh wait, maybe I misunderstood what you are doing. You are editing the default en_UK and fr_FR files, and including your own file instead?
If you include your file at the top, and leave the rest of the en_UK file intact, it will overwrite all of your customizations. You can either delete everything out of en_UK, or else include your file at the bottom. That will then work for the plugins too.
What isn't working?