Hi Boris,
Anse Chastanet has two bays. The first is the main hotel beach, which is a sandy crescent with two rock and coral arms. The southern arm is roped off, as it's a snorkelling/diving reserve, but the northern end of the beach is open. There's a lot of small grunts and snapper that shoal up around here.
If you follow the path round to the second bay, Anse Mamin, you'll see a large disused concrete jetty halfway along. This will probably be your best bet as it's away from swimmers, snorkellers, divers etc. It's over quite deep water but the pilings attract some species. I've had lane snapper and small kingfish from here, the former on small livebaits, the latter on small metal jigs. There's also squid that will take squid jigs.
A local who handlined from the jetty said he's taken large cubera and mutton snapper there on deadbaits at night.
Anse Mamin is rockier than the hotel beach and holds snapper, jacks and small hind (grouper) in the reef. There are needlefish and barracuda in open water - look for the baitfish shoals, which appear like a dark inkstain in the water. Plastics, such as FBMs, work in the reef, metals in open water. The snack bar at Mamin, btw, does incredibly good burgers ...
You can also take the hotel canoes around the bay if that's your sort of thing. Plastics once again will work - jacks, snapper, grouper and needles will be waiting, depending on what depth you fish.
There's a couple of small boats moored on the beach with the hotel's approval and you can haggle with the skippers for a charter. Tbh, it's worth chatting with the ones you like, agreeing a rate, and waiting on the beach till you see the birds feeding offshore, then jump on board and run. It's usually blackfin tuna and the boat will be there in 10min.
You can use decent spinning gear and plastics for the blackfin - they're not huge. Sometimes there's mahi-mahi around too, plus skipjack, jacks and kings. Either that or a 12-20lb class boat outfit.
I wouldn't say it's the best overseas fishing I've had, but there's a few decent fish around and it's a beautiful location. The hotel is excellent too - quirky, good food and terrific service. One tip I'd give you: take your fishing gear, and anything else you need for the beach, when you go down for the first time each day. Forget anything and it's 120-odd steep steps back up to your room ... it's a faff!