The contract was likely formed in the EU country, as it was signed there. If that's the case, the contract is subject to the law of that country. The person in Ireland can be sued in the EU country (under that countries laws), and if a judgment is obtained, then the person can apply to get it enforced in Ireland. At that point it has the same force of law here as an Irish judgment.
If it's a detailed written contract, there is probably some clause in the contract agreeing the jurisdiction disputes will be handled under.