The family and thehave expressed their "shock and dismay" at the High Court's decision not to extradite Ian Bailey to France for her murder.
"The family of the victim have always respected the legislation of both countries, and decisions not always favorable for them.
"Great attention was given to respect Irish legislation and conforming to European Treaty agreements. To which Ireland and France adhere to on equal terms.
"It is not acceptable that this common unilateral legislation is not respected in this instance," a statement from thereads.
"The High Court was not asked to decide if French law complied with European or Irish law. This is already accepted by the terms of the treaty signed by all 27 countries who signed the European Treaty. The nature and reason for the EAW (European Arrest Warrant) is covered by this," the statement continues.
The association, of which Jean Pierre Gazeau - Sophie’s uncle is president, has said that "the High Court of Ireland is not justified in its decision on this ground.
"France is entitled to request the presence of a person to reply to the courts for actions contrary to French legislation. All guarantees of fair judgment by French legislation in accordance with the European Treaties binding all 27 countries is already acquired.
"Therefore the Irish Courts may, at the least, be expected to respect this agreement without further discussion.
"The EAW request for I. Bailey's presence in France is legitimate and guarantees respect and fair treatment in this case.
"France could, no doubt, be encouraged to request, by all means, that the Irish courts respect the agreements signed in the name of the Republic of Ireland and in respect of France, its European partner."
France had sought Ian Bailey's extradition after he was found guilty in France last year, in his absence, of the murder of Sophie Toscan du Plantier in west Cork in 1996. A 25-year sentence was handed down by the French court.
Two previous attempts by the French to have Mr Bailey extradited were rejected by the Irish courts. Those attempts were prior to the French trial held in May 2019.
The first rejection was by the Supreme Court in 2012, with the second rejection being in 2017 by the High Court.