Thank you for the question! It is possible to pay our drivers in Euro, but normally recommend arranging with the payment in the local currency, the Hungarian Forint. The reason is that on the fly our drivers will always say a higher Euro fee than the actual HUF fee, making it better to pay with Forint. Since you anyway need HUF to pay in shops and restaurants elsewhere in Budapest, you should just as well arrange with getting the local currency at once, thus being able to pay our drivers as well with Hungarian Forint.
If you still want to pay with Euro, ask the drier for the current rate.