Would English really use the definite article?
I do not teach my students this usage.
My father-in-law is a native speaker and will always ask waitresses etc if they have 'the gaelic' before launching into unintelligible (until I started this course) conversation!
Is he a native speaker of English?
I teach my students "Do you speak English (Gaelic)?"
Would an English speaker say: "Do you have the English?" or even "Do you speak the English?"
No, he grew up without English until he started school. He's from North Uist.
Correct, you should never use the definite article before the name of a language like that in English. It doesn't just sound weird, it's completely incorrect. Native speakers won't talk like that.
An English speaker would say "do you have the English", yes. Saying someone "has the French" or "has the Spanish" is a common thing amongst old generations in the southern US, especially the really rural and Appalachian areas.