A lawyer for the family of Sophie Toscan duPlantier has described the end of Ian Bailey's High Court action yesterday as an "important step".
Mr Bailey lost the civil action in which he claimed Gardaí conspired to implicate him in the murder of the French film producer.
Her death is also under investigation by French authorities, more than 18 years after her body was found in west Cork.
Lawyer Alain Spilliaert said the investigation there has been held up since last year, however he expects it will now resume.
"The judge should be able to make his last set of interviews during the next few weeks," he said.
"When he will notify to the parties at the end of his investigation, he will then send the file to the Paris prosecutor for review and advice, and then he will send his notification of decision.
"This should be taken by the end of this year."