Been there quite a few times, stayed at that exact site in fact.
All the cycle paths are tarmac or quiet roads.
I have done:
hardtail – fine for pottering about. No offroad that isn’t a sand dune. Don’t do like me and take SS because it will be spintastic unless you up the gears. Fatbike might be good for the sand.
road bike – boring. Biggest climb is the bridge to get there. Plus some drivers get shirty if you don’t ride on the cycle path, which makes it hard to get a good rhythm going. Did see a local chain gang though.
hired a sit up and beg – For pottering to the market / beach / restaurant ideal and no hassle. Not cheap if you add it up for a whole family.
If I was flying I would hire a BSO and take it easy, not worry about getting it stolen, not worry about the right shoes, and a basket to put your picnic in.
Other tips: Avoid driving. The market in Bois Plage is awesome if you like seafood. St Martin likewise. St Martin for harbour side eating and pretending you arrived by yacht. La Flotte is quieter, cheaper, but not as good. The lighthouse is a bit crap but you will go anyway on the day it rains. Bois Plage is the best beach so don’t bother finding another. The kids will like the odd chocolate shop in the middle of nowhere.