I travel a fair bit with this in mind, so I make sure I'm covered, in a few lines ......
A Credit card with NO fees for any Euro transactions = The Post Office Credit Card, underwritten by the Bank of Ireland. Top drawer customer care and no hassle, I use them a fair bit now (Euro zone).
Credit Card with FREE anti fraud cover, cash back, and "day exchange rate" with no transaction fees = Capital One, I use them in the USA. They are really hot on anti fraud. This card has worked in every hole in the wall on every continent (except the Polar caps, I ain't been to them 8ree!)
Best bank account with 24/7 concierge service overseas with Visa card etc = Nat West Private Banking, but that isn't cheap, the annual service charges arebrok3, but the perks are worthwhile.