The word 'portemonnee' comes from the French "porte monnaie"; porter: 'to carry' and monnaie: 'coin'. :)
It's a wallet (so a BE purse, but not an AE purse). I think a coin purse would be beurs* in Dutch, but I never have heard anyone using that word (in the meaning of a coin purse).
We also have this thing called 'portefeuille'. It looks a bit like a 'portemonnee', but instead of coins and banknotes, we usually put cards and important documents (like your ID, debit cards, driving license, etc.) and sometimes banknotes inside.
We can put our ID and other cards in our portemonnee as well, so it's a bit confusing. :P