The SiteLabel control is designed to make it easy to use resource files. You just set the ResourceFile and ConfigKey properties either decalratively in markup or using code. The control will lookup the text to display by finding the key inside the resource file.
Resource.fr-FR.resx would be used for translating core mojoPortal labels to french. You should not put your custom text in there, but instead create a new resource file in your external module and copy it to Web/App_GlobalResources in a post build event.
So you might make a MyCustomApp.resx for english labels and MyCustomApp.fr-FR.resx for French labels. You would set the ResourceFile property on SiteLabel to MyCustomApp, you don't include the fr-FR or the .resx.
See how this is done in the WebStore app? It has WebStore.resx in its own App_GlobalResources folder and this gets copied to Web/App_GlobalResources during post build event.
Hope it helps,
Joe