Well, it's interesting you have chosen 1660-1670 as your target. This would be the period when Louvois, Louis XIV's Minister of War, would be trying to replace matchlocks in the army with flintlocks. And that's what a fusil meant: a flintlock musket, instead of a matchlock or snaphaunce. And that's what the French had invented earlier in the century, when one of the gunsmiths resident in the Louvre ( usually thought to be Marin le Bourgeoys, who also made clocks) had created the flintlock for the resident gun collector, Louis XIII. But that's circa 1608, and though the commercial gun market would have fine flintlock sporting guns by 1640 ( some even with very clever things- breechloading, double-barrels, water-resistant locks) mere soldiers and poor people could be trudging around with matchlocks well past Louvois' time, and not just the Spanish. Louis de Gaya's 1678 Traité des Armes illustrates the position of a musketeer with a matchlock- and one that only has a firing lever, doesn't even have a trigger & triggerguard. His book shows a fusil, also...but his model musketeer has, still, a matchlock.

So, it's a reminder that this was a necessarily frugal time. Because guns weren't yet made in mass ( some economies of scale in production would come in the next century) like most made things, they were expensive. The English were happy to send a lot of outmoded junk to their North Atlantic colonies, for the colonists defense, and you would expect that a lot of similar junk would be in the Caribbean. What would L'Ollonnois have hanging in his belt? Would he have a snaphaunce , wheellock or flintlock? Would his crew have French fusils, arquebuses, mousquets ? The questions would have to be , what was available that he could have stolen? What did he have money to buy? Pirates also do not seem, on the average, to have been a very wealthy bunch. Unless there's a detailed period account for your person, place and time period, that's going to be hard to definitively answer. But if you wanted to draw a picture of a boucanier, c. 1670, you could plausibly show him holding any of the above.

However, as far as locks are concerned, though the English would at mid-century add the dog to their locks ( and also add the bridle and the one-piece sear, two things that made the lock function much more smoothly) the half-cock notch seems to have been a feature on French flintlocks even before then. Those English dog locks would commonly have half-cock notches as well. The English today would call that the "belt and braces" approach to a safety.

Torsten Lenk : The Flintlock

J.F. Hayward : The Art of the Gunmaker v. 1