Cash-only is rare. L’Esprit had no phone service at Thanksgiving, so could not accept credit cards. They may have phone service now. Le Saintoise in Corrosol was cash-only for awhile, but now has phone service and is again able to accept credit cards. Bar de L’Oubli has said No Credit Cards on their menu for years. I don’t think that Le Select has ever accepted credit cards either. That’s all that I’m aware of.
On the credit card note, if you're an AMEX user, make sure you also take a MC or VISA. Some places won't take AMEX and those that do may give you an unfavorable exchange rate, but will tell you in advance of that and encourage you to use a different card.