There are several credit cards that don't charge an extra fee for "International Transactions". Two that I'm aware of are Chase Sapphire and American Express Platinum, but there are others.
However, International Transaction Fees are not the only cost to consider. Some banks (who are skilled in the art of deception) extract "hidden fees" in the form of exorbitant exchange rates relative to the "Interbank Exchange Rates" (IB rate). Both AmEx Platinum and Chase Sapphire charge exchange rates that are fractions of a basis point above the IB rate. Some others will charge hundreds of basis points above the IB rate - this is something you must investigate before you apply for the card.
And before leaving the subject of exchange rates: When you use your US card overseas, you will occasionally be asked if you want to conduct the transaction in Euro or Dollars; THE CORRECT ANSWER IS ALWAYS US DOLLARS! Why? Because the "processor" handling the transaction will charge you 5% or more above the IB rate, then pass the transaction to your card company in US$!
Unfortunately, the "best" cards seem to come with a tradeoff in the form of "Annual Fees" charged by the institution issuing the card. AmEx charges a hefty annual fee (ridiculously high really) for their platinum card; but giving credit where due, there is no card that will protect you better than American Express. When I say "protect you", I mean that if you are sold shoddy merchandise, or merchandise you ordered was never delivered, or whatever, you can file a dispute. Of course you can file disputes through Visa and Mastercard banks also, but their arbitration rules somehow always seem to favor the merchant. Not so with AmEx - most of the disputes I've filed with AmEx wind up as credits to my account in a fairly short period of time. The Chase Sapphire card has lower fees than AmEx Platinum, but their dispute arbitration rules are VISA's rules as this is a VISA card.
Another significant difference I've noticed is in card replacement policies. There is a fair chance that at some point in your overseas stay you will have to have your card replaced. This may happen for a variety of reasons; usually related to fraud. AmEx Platinum will overnight a replacement card to you at no additional cost. If you're in a large city (where overnight service is available), you won't be long without a card. Chase won't pay for overnight, but they will get a replacement card to you in a few days. Other card companies WILL NOT SEND A REPLACEMENT CARD TO AN OVERSEAS ADDRESS! And that can be quite inconvenient of course. Another question to ask before applying for a card.
And one final point to make: Most merchants I've dealt with in Europe and the UK will take credit cards. However, you will encounter merchants that do not accept AmEx... I guess being a "consumer friendly" card has its costs, and some merchants decline for obvious reasons. The long and short of this is that one card really won't do - you'll need two.
Hope this helps - let me know if you have questions.