The short answer to your question is that you will use the Euro to USD exchange rate, if your foreign financial accounts are denominated in Euros. The reason is that you need to convert the foreign currency (Euro) value back into your "functional currency" (USD), for tax reporting and compliance purposes. A longer answer to your question requires further explanation.
In order to answer the disclosure questions asked by the IRS and the larger US Treasury Department (FACTA and FBAR requirements), you can use the midpoint, or average, of the total range of the Euro to USD exchange rate applicable during the calendar year. There are many places on the internet where you can look up such historical values for any currency pair, so that part should be fairly easy and purely mechanical.
Also, it is helpful to note that the foreign exchange conversion rules also apply to purchases and dispositions of any capital asset or other investment, and not just simple bank accounts. In other words, you'd apply the exchange rules to stocks, partnership interests, real property, mortgage payments, etc.
You may additionally benefit by reading a more detailed discussion of foreign exchange rates, as can be found at the following AnswerXchange post:
Additionally, there are two separate disclosure forms that may be required for foreign financial accounts owned or controlled by US taxpayers; each also has different reporting rules. One is known as IRS Form 8938, and can be attached to the relevant yearly Form 1040 tax return. The other is FinCen Form 114, which can only be filed via the internet. The following Internal Revenue Service webpage describes them in some detail, and provides their dollar value reporting levels:
Form 8938 is included in TurboTax. FinCen Form 114 is not included in TurboTax, and you would need to access that reporting webpage separately, if your foreign financial assets total over the limit(s). Note that you can get to the FinCen reporting internet site directly through the above IRS link.Thank you for asking this question.