We try to bring whatever cash we think we are going to need and avoid the ATM issue. We haven't stayed in Grand Case since 2014 but I don't recall there being any ATMs in Grand Case. The one time we had to go to one, we had to go to Marigot.

Many businesses and restaurants take credit cards (Visa/Mastercard primarily) - just make sure that you contact the credit card company before you go so that they won't deny charges.