A former INLA prisoner who was involved in the search for Seamus Ruddy has said the remains found at the weekend were less than 40 yards from a previous search site.
Mr Ruddy, 32, was murdered and secretly buried in 1985 by the Irish National Liberation Army (INLA).
Willie Gallagher has been liaising with the commission set up to find the bodies of the Disappeared.
He passed on the new information which led to the discovery near Rouen.
Formal identification has yet to take place.
Mr Gallagher, of the Irish Republican Socialist Party (IRSP), said a decision to follow up on a rumour about an INLA arms dump in a forest provided the breakthrough at the weekend.
The former INLA man, who was jailed for a bomb attack on a bar in Strabane, said he is relieved the search is now over.
"Three years ago we had extra members on our team to re-examine and re-evaluate all the information we did have and during the course of that we came across what seemed an insignificant rumour which we pursued," he said.
"That insignificant piece of information provided the key to lock the door with regard to more precision as to where the body was and we were successful in the recovery.
"We chased down every lead possible, and some of those leads came to dead ends and actually involved a number of us travelling over to France, Belgium and Spain."
Anne Morgan was the only member of her family to travel to the search site in France.
Before attending Mass at the Church of Joan of Arc in Rouen on Sunday morning, she said she would "be thinking of family" who were at home.
"I'll also be thinking of those who have been here looking after this site at Pont-de-l'Arche, and all of the people who have spent a lot of time helping us to find Seamus."
Mr Ruddy was working as an English teacher in Paris when he went missing.
He was one of 16 people known as the Disappeared who were murdered and secretly buried by republicans during Northern Ireland's Troubles.
The INLA admitted responsibility for the killing 10 years after Mr Ruddy's death.
This latest search began in France on Tuesday after new information was passed to the Independent Commission for the Location of Victims Remains (ICLVR).
Other members of the Ruddy family were at home in Newry, County Down, when the discovery was confirmed.
The remains of three people out of 16 Disappeared have not yet been found.
The others are Columba McVeigh, Joe Lynskey and Army Capt Robert Nairac.