Bring lots of sunscreen!
There are Metropole-style pharmacies which carry top of the line French sunscreen, that can be expensive.
Also, keep hydrated, especially when hiking in the mountainous areas. A hat is often a good thing to have because the sun can get extremely hot.
See the above mentioned section. Heat prostration and sunburns can be a real threat to those not used to the climate.
Mosquito repellent is a good thing to have if you are sensitive to bites. There is no malaria on this island but other mosquito borne diseases such as Dengue Fever are present.
respect
Polite manners will go very far in this jewel of the Caribbean. When entering a business establishment, always say, 'Bonjour' and 'Merci, au revoir' when departing. Also note that things often run a lot slower in warm climates, so patience is a must. Also, don't expect kowtowing, smiling 'natives'. The Martiniquais are a very proud, dignified people and are often wary of impatient tourists without manners.
Unaccompanied women in tourist and beach areas are likely to experience frequent cat-calling and similar attention from men. A popularly stated reason for this is that there are a greater number of women than men on the island. The best way to deal with unwanted attention is to ignore the attention or firmly state a lack of interest.