If you use your credit card abroad, the amount will be exchanged from Euros. The exchange rate is set by the network (Visa/Mastercard) and will be more or less equal to the „official“ rate (interbank exchange rate).
Your bank can charge fees on top of that, both per-transaction one-time fees or a percentage. There are also some cards that have no fees at all. My bank charges 1,5%, for example.
The fee will not be on the merchant receipt, as it is charged by the bank. The merchant receipt will be in Forint, and your credit card statement will show the amount in Forint and the converted Euro amount. At least for me the fee is a separate item on the credit card statement; but it is clear that it is for the same merchant.
Some merchants also offer to „pay in Euro“. This is more or less a thinly veiled scam, as the exchange rate can be something like 5% (or more) worse than the interbank rate. Meaning that the „free“ service has a 5% fee. If you use this „service“ you get a merchant receipt that shows the Forint amount and some information about the conversion. Your credit card statement will just show the charge as Euros.