'The' becAuse you are talking about 'the euro', not any old euro in general, but a specific currency with specific attributes. The Cdn dollar, the US dollar, the british pound - all refer to a currency, not a piece of currency in your pocket.
You can often replace 'one' with 'a' or 'an' to get a better idea of which article makes more sense in a given context .
Just to confuse things however, Colloquially, the two (a or the) in this case would likely be interchangeable in spoken language.