Note first that the stand of trees in your photograph, as to be expected, did not exist when the fort was in use
Then, note that to our left and due east of the fort is first an overgrown ravine, then a sloping hill about 30 feet higher than the fort. Artillery here would have quickly demolished the wooden stockade, and had a clear view of the entire fort as well as the small community west of it.
The coup de grace would then be done by infantry advancing down the peninsula to the fort, and possibly also from the point south west of the fort.
For the garrison as listed, and assuming no great difficulty trekking overland to the fort, then an infantry battalion, two artillery batteries, and a squadron of dragoons should not have difficulty investing and capturing the fort with modest casualties.
The more interesting problem is if the assault must be done amphibiously. As "A ship's a fool, to fight a fort", it would be necessary to find a suitably close location for disembarking out of range of the fort's guns. I'll leave that for tomorrow.
The wooden stockade and towers, more than a century post-Vauban, are clearly not intended to defend against a serious assault, or capable of doing so. They are sufficient only to protect against a coup de main and force an assault of some sort. They are a delaying tactic; intended only to buy sufficient time for stronger defensive forces to assemble and arrive.
Assault force Assumption
- Naval: 1 Frigate, 2 sloops/brigs, 1 transport
- Land: 1 infantry battalion (~600 men), 1 dragoon squadron (~120 men), 2 9/12-lb field batteries (~50 men), ship's marines from crews above (~80 men), additional ship's guns as needed. (most commonly 12-lb, but possibly 18-lb)
From the Point North of the Fort
- Blue Beach, right in front of the fort, will be too well covered by the fort guns to be usable until they have been suppressed. However the threat of landing here is usable to suppress sorties from the fort attempting to interfere with a landing at Red Beach. The two brigs/sloops and the combined ships' marines will stand off here, out of fort range, making this threat.
- Red beach, ~1200m WNW of the fort, will be the primary landing zone - but look at those breakers. The frigate and transport will disembark here using skiffs, covered by the frigate's guns.
-Gun emplacement A overlooks the fort by about 15-20 feet, at a range of ~400m; just out of effective canister range. Once your guns are setup here you request, and will receive, honours of war. It is very unlikely that a wooden stockade, outnumbered 4-1, will defend to the death once opposing guns are emplaced here. The defenders will not be fanatical patriots such as at the Alamo.
The Details - Emplacing the guns
Outnumbering the defenders 4-1 with the advantage of greater artillery and cavalry, advancing across a flat plain devoid of significant features is not a challenging military operation. The brigs are still standing off Blue Beach threatening a coup de main against the forts' guns if the garrison attempts a significant sortie. There will be casualties, but my expectation is about 30-40.
The biggest challenge will be being patient enough to wait for suitable wind, tide, and waves. This looks to be a lee shore, and a rushed landing could result in loss of one or more vessels on those rocks. The fort is well situated, defending the friendliest landing beach for miles around. However once landing conditions are suitable, I suspect that less than 36 hours would be needed to entice a surrender with Honours of War.
My guess is that thee were originally plans for a larger fort on the larger point, which might have been a truly formidable structure, but economics never became justified.
Realities of War
In an actual scenario, the assault force will not be quite the one listed above. The infantry battalion will have the grenadier company, and maybe one fusilier company, detached for another operation. Only one brig will be available in the requisite time frame, and the frigate will be a small 32-gun frigate with only 9-lbers instead of the desired 18-lbers. A commander must make do with what he has got. The garrison is probably under-strength somewhat as well. Accomodation must be made, and time frames may slip a bit in consequence. That is the reality of war. Perhaps a spy has been slipped into the fort, and a night-time coup de main is in consequence conceivable at Blue Beach. Remember that the normal crew of a brig is half as numerous as the full garrison of the fort, and a brig is a very seaworthy vessel; in calm weather one could easily be overloaded briefly with 2 or 3 hundred soldiers. Have fun with this.