Anse A La Mouche is a lovely wide sweeping bay, offering great views and scenery but perhaps not the best beach in the area, as the waters here are relatively shallow and high tide claims a lot of the sand. There are multiple spots along the bay where you can take a dip or relax on the sand but the bay doesn't form a continous stretch of beach like Baie Lazare or Anse Takamaka to the south. The beach is backed by the Anchor restaurant as well as various smallholdings and farms, one of which offers a great organic fruit and veg farm shop. If you time it right you could find the local fisherman selling their catch of the day by the roadside.
There's also couple of local stores and a number of self catering places smattered around the bay, some of which boast incredible views. The village also marks the turning point for the Chemin Les Canelles across to the east coast, which is an easier climb and shorter crossing than Chemin Montagne to the north, and less wild than the south road between Quatre Bournes and Anse Forbans.
All in all Anse A La Mouche is a good base for exploring the south west if you have your own transport, and is very convenient if you are self catering, but you may find the beach a little disappointing if you're not planning to head off on adventures each day.