I think you're ok. I don't know anything about B of A and BNP, but there are a lot of BNP branches around Paris.
You'll have to go to the window at the RER station based on posts by others who say the machines there often don't take US credit cards. All the RER and Metro stations I've gone to take US cards (unless their equipment is down), though sometimes I have to ask them to keep trying as they don't know how to use the US card.
Cap One works but before you go, push through their prompts to the automated process that records when you'll be out of the country and where you're going. They still may decline a charge and ask that you call them so take a back-up. Schwab has a much better product and service that gives 2% back-see thread under Other Credit Cards.