If you're serious about doing freelance work on a business basis, then you always should be prepared to invoice in the currency of the customer. That's not only good business practice, it's also a basic courtesy.
That said, if you are dealing in small amounts, and the client's currency is not that of your own country, you could lose a lot of money in paying for bank transfers and currency conversions. One solution to that is to open bank accounts in the currencies in question, but that's not really practical if you are dealing with more than a couple of currencies.
As a minumum, you should consider offering the option of billing in euros and US dollars, and running bank accounts in those currencies.