It is generally the case that an electric current should begin to flow when two different metals come into contact, especially if are immersed in salt water. There is a potential difference (a voltage) and one metal passes electrons to the other metal while it corrodes.
The one and two Euro coins are made up of two different metals, so it would be logical to expect a flow of electricity and consequent corrosion. However, the gold-and silver-colored portions of the coins are made up of very similar alloys and so don't really have any significant potential difference. The gold-colored part contains 75% copper,20% zinc and 5% nickel, while the silver part is made up of 75% copper and 25% nickel only.