Agree with all above. My general rules for the French side:

1) If the place accepts credit cards, and doesn't do 1:1 cash, use the card and charge to the local currency (euros) to get the best exchange rate.

2) If the place does 1:1 pay cash, use dollars (Beach chairs at Orient, and Super U sometimes offers this!).

3) If the place is cash only without 1:1 exchange, pay in euros to get best deal, but I don't sweat it if I only have dollars since I don't mind paying a bit more for convenience; Friar's Bay Beach Cafe is about the only place I can think of where this might come up among the places I frequent.

Of course I use cards without foreign transaction fees. And I keep euros from trip to trip so I don't worry as much about the ATM fees.
Our group typically takes turns paying with credit cards when rule #1 applies (most restaurants) so most of our dollars end up circulating between us during the week, which keeps things pretty balanced for us between using cards and cash.

Having Credit Mutuel back online in Hope Estate with the choice of dollars or euros makes life a lot easier now, the post office on the other side of Grand Case only does Euros.