TL;DR - Gaelic
So a ship of pirates in the golden age of piracy was certainly a motley crew, but I doubt they were very mixed "nationally", except maybe toward the end.
Most piracy in the 1600s were one man's pirate is another man's privateer and were national naval militias fighting it out...well, strange story, but none-the-less.
I want to argue that English pirates, more accurately "British" pirates, spoke Gaelic.
First, until 1614, over 1,000 recorded pirates were West-Irish sailing from Ireland. Until the Dutch blew the hell out of Crookhaven. Only 180 of the pirates were engaged and most captured, seeking pardons. The others arguably fled to the Caribbean.
Not long after that, the English Civil Wars, the Cromwellian Protectorate invading Ireland, and later, the early 1700s decree that all Scots should speak a form of English, that together with the Jacobin rebellions, led more Gaelic speakers to flee to the Americas.
So, while it's been hard to FIND actual documentation on this :-| I argue if you were aboard an "English" pirate ship the more likely language you'd hear is Gaelic.
Gaelic was the majority language of Ireland (almost 100%) until 1800, and was about 100% majority language in Western Ireland until 1870s.
I found somewhere else that 25% of all pirates in the fleets from 1500 - 1717 (end of golden age of piracy) were Irish, specifically.
That's quite huge demographic considering pirates were Huguenots, French Catholics, Spaniards, Mexican-Spanish, Natives, Blacks from their various regions, Portugues, Dutch, German and yes, some English, too.
It's no mistake that Blackbeard chose Queen Anne as his flagship name. What was she avenging? It was likely named for Queen Anne being the last Stuart monarch which is also a Scottish dynasty and were known for learning Gaelic gasp against the wishes of the English noble class, although that tradition petered out by Queen Anne's time.
Still, just an odd-ball fact.
Except for England itself, and the nobility across the British Isles, Gaelic was the common language for everyone until about 1650 when it started to split in favor of English for the commoners for lowland Scots and North Irish protestants.
