I can’t find any recordings of him speaking English, but here’s an English interview with his son, the (former, at the time) Crown Prince.
How well do Spanish Royals speak English? Is Filipe atypical?
No, Felipe is pretty typical not just of his family but of “Spaniards who have actually worked at their English” in general. We still can detect each other across a full train wagon (I can actually hear slips in that particular speech you linked, for example), but there comes a point where that’s got more to do with being obsessive about it than with our English actually being “bad”; him and most of the Spanish royal family are there or one point below. Juan Carlos has a speech defect in Spanish, I assume it will show in his English as well, but it boils down to “if he’s not careful, he sounds like he’s got his mouth full”; his grammar, vocabulary and usage will still be perfectly fine.
Royals are generally reared with good language skills because (a) it’s foreseeable from early in life that this will be useful to them, and (b) they tend to come from families which are, linguistically speaking, fairly cosmopolitan.
With elected heads of government and heads of state, it tends to be a bit more hit-and-miss.
He’s not very good. Slightly better here. Pretty heavy accent. So, yeah, he speaks English about as well as his wife speaks Swedish…
True dat. Wonder how consort’s English is then. Queen Letizia was a commoner , but a former newscaster. Hers might be good. How do Dutch/Belgian/ Scandinavian consorts hold up.
Henrik, the Prince Consort of Denmark, mainly refuses to speak English, “so as not to feel colonised.” The guy is French, if that makes a difference… 
execpt in Belgium, where the royals seem to have trouble learning the language of half their population(Flemish)
Mark Rutte speaks English fairly well. Fredrik Reinfeldt the former Swedish PM also speaks fairly flawless English.
That’s an understatement, she sounds like a native British English speaker.
I hear a clear Danish accent there.
Same with Reinfeldt - a very clear Swedish accent. Also, fun moment when he says “ninety-nine point fem, uh, five, percent,” fem being the Swedish word for five. 
Usually if you’re referring to the ethnic group, you’d capitalize the N in native, and/or use a hyphen (i.e. “native-american”).
Political correctness aside, with so many companies outsourcing their tech support and customer service call centers to India, it’s no longer obvious which “Indians” a person is referring to.
My response about the Spanish royal family included consorts and ex-consort (Marichalar’s English is better than Elena’s, or at least it was before his TIA).
Untrue, of course. The term native American does not mean an American Indian. A Native American is something different.
Merriam Webster:
Native American
: a member of any of the aboriginal peoples of the western hemisphere; especially : a Native American of North America and especially the United States — compare american indian
As far a the term being “hijacked by the PC crowd,” the first use of Native American in the above sense was in 1737.
Not quite - the accent is still there and I don’t think I would ever take her to be British but the word choice and grammar in conversation - not just in a set speech - is spot on. See this clip where she is talking to Kirsty Walk on Newsnight .
Really? I don’t think she sounds like a typical Dane speaking English. Where her accent does come through the pronunciation is well within the normal range of British accents.
I went to English boarding schools until I was 14, but I have an American accent. I developed it after boarding school, though. Beyond that, there were lots of kinds from Hong Kong at the schools I attended who never lost their accents (though they became less pronounced.)
I remember one news reporter (Mike Wallace?) commenting that 1970s West German Chancellor Helmut Schmidt spoke very good English, except for slightly mispronouncing the word “deaf”.
Her Danish accent is very obvious to me.
When listening to George W. Bush you really need a Bush to English dictionary at hand.