The jobs you saw for A320 based in Dublin are probably with Eirjet. If and it is a big if, EI use contract pilots they will probably use Parc as they used to own them and have used their services in the past, by the way EI would only be looking for contract co-pilots, they never have employed contract Captains or taken direct entry Captains. As regards being a non-national, that is not a problem as long as you have "the right to live and work in the EU". We have French, Dutch, American, Canadian, Kiwi, Finnish, Scots as well as loads from the UK ( sorrry if I left anyone out!) flying with us.
I`d suggest that you fire in an up to date CV to the personnel department, Address should be on the website. Best of luck!!