Lawyers for runaway teacher Jeremy Forrest said the "full story" of his disappearance with a teenage pupil will emerge after he agreed to his extradition back to the UK.
Forrest, 30, appeared before magistrates in Bordeaux today, four days after he was arrested on suspicion of child abduction.
The married maths teacher from Ringmer, East Sussex, travelled to France with 15-year-old pupil Megan Stammers on September 20.
A European arrest warrant was issued after the pair failed to use return ferry tickets three days later.
Forrest's UK solicitor Phil Smith said after the court hearing: "Now that Jeremy has agreed to be extradited back to the UK we look forward to the full story emerging in the coming months.
"He is very appreciative of the support and assistance given to him by his family and in particular his parents."
Forrest, who appeared in court wearing a T-shirt, checked shirt and trousers, confirmed his name and nationality before agreeing to return to the UK.
Flanked by an interpreter and two security guards, he signed a document to kick-start extradition proceedings during the short session.
The court is expected to give the green light to his removal from the south-western port city on Thursday.
Mr Smith from Tuckers solicitors said: "Naturally, Jeremy is most concerned about the impact of this episode on all those affected.
"He will be making no further comment whilst the judicial process takes place and is co-operating with the authorities."
A lawyer at the court, who did not want to be named, said it was likely that Forrest would be returned as soon as the French magistrates rubber-stamped the extradition.
Forrest, Megan's teacher at Bishop Bell C of E School in Eastbourne, was being kept in detention until his removal.
The teenager has already returned to her home town and been reunited with mother Danielle Wilson and stepfather Martin Stammers.
Megan was reported missing when she failed to turn up for school and it emerged she had travelled to France with Forrest, sparking a highly-publicised search.
The pair were spotted on CCTV cameras on a cross-Channel ferry from Dover to Calais and later tracked to Bordeaux where they were recognised by a member of the public who had seen television coverage of the case.
Amateur musician Forrest was arrested there on Friday.
According to reports, he touted a bogus CV around bars in the city as he sought cash-in-hand work.
Before her disappearance Megan told her mother that she was going to spend the night at a friend's house.
Her mother said Megan was "really excitable" and was "jumping around".
A message was later sent to one of Megan's friends saying she had arrived safely in France.
The investigation was ramped up when she and Forrest failed to use return ferry tickets on September 23.
A European Arrest Warrant was issued and the case featured on BBC's Crimewatch.
Online pleas were made on Facebook and Twitter by Mr Stammers and her siblings.
Forrest's father Jim, who lives in Petts Wood, south east London, also made a public appeal for their safe return.
It emerged that Forrest gave Megan extra-curricular maths lessons and that concerns about their closeness had been reported to the school authorities following a trip to LA in February.
Forrest was due to be suspended by the school the day before he and Megan went to France, it has been claimed.
East Sussex County Council has confirmed it and school officials were "addressing and investigating concerns" but has not said when those were made and declined to comment on suggestions he was facing suspension.
Megan's headteacher, Terry Boatwright, said the school would offer support to the teenager and her family "as they seek to return to some sort of normality".