My understanding is that the "Archipelago Frigates" were basically Baltic variations on the xebec, which is similar to what the Corsican Navy already uses. The Corsican polacres (Lacedemone and Idra) are square rigged, unlike the lateen rig of a "true" xebec, but the actual construction of those ships are very similar: a low, lightly built hull with a narrow waterline and broad beam, and single piece "pole masts" rather than the multi-part masts of other square-riggers. As for the hemmema, a 36-pounder main battery on a 26-gun ship is frankly rather insane and makes me think that they probably weren't "xebec-built" in the traditional sense, because no Mediterranean xebec I'm aware of could handle that kind of artillery without destroying itself.
Carronades would absolutely be useful to the Corsican Navy. The favored tactic of the Barbary corsairs was boarding, which they facilitated with overly large crews, sometimes stuffing 300 well-armed men into a rather modestly-sized xebec that in another navy would have had fewer than 200 crewmen. A low, lightly-built ship closing to boarding range with its deck crowded with men is basically the ideal target environment for a carronade, and at the very least replacing the QD/FC guns with carronades would make perfect sense (although the Navy's current corvettes are all flush-decked and don't actually have QD/FC guns). They would also be helpful for the Navy's small auxiliary ships; an 8-gun cutter with 12pdr carronades is much more dangerous than the same ship with 3pdr long guns. At the moment, however, the Navy is not exactly flush with cash, and given Corsica's alignment with the Bourbons during the recent war, I doubt any would have made their way to Corsica during that time. In the future, however, they might certainly find their way into Corsican arsenals.
Carronades would absolutely be useful to the Corsican Navy. The favored tactic of the Barbary corsairs was boarding, which they facilitated with overly large crews, sometimes stuffing 300 well-armed men into a rather modestly-sized xebec that in another navy would have had fewer than 200 crewmen. A low, lightly-built ship closing to boarding range with its deck crowded with men is basically the ideal target environment for a carronade, and at the very least replacing the QD/FC guns with carronades would make perfect sense (although the Navy's current corvettes are all flush-decked and don't actually have QD/FC guns). They would also be helpful for the Navy's small auxiliary ships; an 8-gun cutter with 12pdr carronades is much more dangerous than the same ship with 3pdr long guns. At the moment, however, the Navy is not exactly flush with cash, and given Corsica's alignment with the Bourbons during the recent war, I doubt any would have made their way to Corsica during that time. In the future, however, they might certainly find their way into Corsican arsenals.