Yes, this construction works for other countries—and for other locations—as well. (Think 'Straight Outta Compton' for an example as Béarla.) But for your specific example, it would be Is as an bhFrainc dó, because 'France' is an Fhrainc ('the France', as you'll encounter in topic 'The World').
An idiom is a word or phrase that people understand in a particular way, even though it doesn't necessarily mean what it says literally - "to kick the bucket" is an idiom. Every one knows that it means "to die", which has nothing to do with buckets or kicking.
Is as Éirinn é and is as Éirinn dó are both understood to mean the same thing - "he/it is from Ireland".