I think if I was travelling to Europe again, I would pay the merchants directly using my card as often as possible and get the big-bank exchange rate. In the US now, you can almost always pay by card; I don’t know about Europe though.
When I was in the U.K., I would withdraw my monthly rent in British pounds from the ATM using my Navy-affiliated CU credit card at the beginning of the billing cycle.
My CU would charge my card the market exchange rate for that day, no fees. I would pay off the balance at the end of the billing cycle, using my military housing allowance, no interest charges.
Worked out great. Also did the same in South Korea.