Lawyers for Ian Bailey have begun making an application to the High Court for leave to appeal to the Supreme Court the decision to extradite him to France.
Mr Bailey is wanted in France in connection with the death of French filmmaker Sophie Toscan du Plantier in Cork 14 years ago.
His lawyers said the decision to extradite him was unprecedented and the Supreme Court should be given a chance to consider it.
The High Court heard that every Irish citizen is facing a stark new reality of possible prosecution in other jurisdictions following the decision to extradite Ian Bailey to France.
Mr Bailey’ lawyers said the decision to extradite him was unprecedented and raised questions of exceptional public importance.
They said the multi-judge Supreme Court should be given an opportunity to consider it as the law in the area was not settled.
Mr Bailey's application for an appeal is based on the interpretation of parts of the European Arrest Warrant Act 2003 and the Criminal Justice (Terrorist Offences) Act of 2005.
Senior Counsel Martin Giblin said every Irish citizen was affected by the decision.
Mr Giblin said Irish people may now be viewing Europe in a very different light and could be unaware of the provisions of European Arrest Warrant Act.
On the current interpretation by the High Court, he said any Irish citizen involved in a traffic accident with a French tourist could be ‘shipped off’ to France for prosecution if the DPP here decides not to prosecute.
‘Every citizen is in the firing line’ he said.
Similar situations could arise in the event of violence after a football match where a French citizen was injured because of France's claim to extra territorial jurisdiction.
He said the State's obligation to surrender citizens under European agreements had to compete with the rights of a person and in many cases the rights of the person could superseded the international obligation.
Counsel for the State Robert Barron said the application by Mr Bailey did not raise points of exceptional public importance but applied only to the facts of this case.
He said the same set of circumstances were unlikely, if ever, to arise again.
He said the application was an attack on the European Arrest Warrant system and the French republic.
Mr Justice Michael Peart will give his decision on 13 April.
