VGFacts

As if Pirates! Gold using pieces from Johann Sebastian Bach in its soundtrack wasn't interesting enough, the 2004 remaster of Sid Meier's Pirates! has potentially more musical references to put on the table.

The leitmotif of the English (heard in their ports, taverns, governors' manors, etc.) is a cover of "The British Grenadiers", a traditional military march of both the United Kingdom and Canada.
For comparison, here's two English themes from Sid Meier's Pirates!:
And here's two versions of "The British Grenadiers" in one video:
I'm not sure if there are similar references in the French, Spanish, and Dutch leitmotifs, as they don't sound particularly familiar.

[UPDATE FOR THE ACCEPTED TRIVIA]

So the English leitmotif is actually two songs, the first being the aforementioned "British Grenadiers", but about halfway through, it switches to "Drewries Accordes", another song from England's musical history.

I still have yet to figure out the French, Spanish, and Dutch leitmotifs, though.

Sample of "Drewries Accordes":

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[ADDITIONAL TRIVIA]

While sailing with high crew morale, you can hear your shipmates singing in gibberish. Despite the nonsense lyrics, though, these are the melodies from two famous sea shanties, "Blow the Man Down" and "Drunken Sailor"

Shanties from Sid Meier's Pirates:
The shanties they're based on: