it wouldn't be a small addition to do this, and would require considerable hand coding.
the product insert and updated pages would need to have a new form element added for the Euro price, and you would need to edit the insert and update record behaviors to use that new form element.
you would need to modify the login to store the users country in a session variable
on the product pages, you would need to create an if statement to show the proper column based on the session value
and you would need to edit the eCart add to cart code to use the correct price column based on the session value.
you would also need to edit the eCart code for sending the transaction to the gateway to use the correct currency code, and edit the shipping behavior code to use the correct currency code