In December 1996, the body of Mrs Toscan du Plantier was found outside her holiday home in Schull, West Cork.
The French filmmaker had been beaten to death.
Ian Bailey has become a suspect but has never been charged with his murder in Ireland and continues to insist he had nothing to do with it.
In his absence, a Paris court found him guilty of murder last year and sentenced him to 25 years in prison.
Armed with this conviction, the French authorities are now asking for his surrender for the third time.
The 63-year-old will find out this afternoon whether the High Court in Dublin will approve his request.
Reportage de Frank Greaney