There are indeed a bunch of hardcore anglers on this forum as well but I don't think they are in Mauritius at this time of the year.
Although you're staying in the NE part of the island, you don't have to limit your fishing to that part only and I hope you get the chance to go to Grand Baie (NW), Black River( West) where there are big game fishing specialised firms. I'm sure your hotel will be able to advise you when you get there.
I'm not sure you will be able to rent a boat all for yourselves but you will be able to rent one with a skipper in it (new law or something like that). Just think of him as a guide. What I used to do is to pay some money to a local village fisherman to take us the whole day the last time I had some mates over to visit. However that was in the South part at "Le Morne"
No you won't get over 10lbs casting from the beach. You can get 15-20lbs in the lagoon if you're lucky (in a boat obviously) but the biggies are in deeper waters. Did some search on the yellow pages for you:
You might try these.
I miss fishing so much.....can't really fish here in the NE of England with this crappy weather :D