The foreign transaction fee will remain the same percentage of the amount regardless of the exchange rate, but the exchange rate might affect the final amount you’ll pay.
The exchange rate is the rate at which one currency can be exchanged for another. Each payment network has its own conversion rates that may differ slightly between different payment networks or banks.
For example, at the time of writing, $1 is 0.91 euros. If the foreign transaction fee is 3%, for a purchase of 100 euros, you will pay a $3.30 fee. However, if the exchange rate changes to $1 for 0.93 euros, you'd pay a $3.20 fee.