Maths teacher Jeremy Forrest agreed to his extradition at a hearing in the port city on Tuesday.
His British solicitor said the "full story" of his disappearance with 15-year-old Megan Stammers to France will emerge once he has been returned to the UK.
Phil Smith of Tuckers Solicitors said Mr Forrest was "most concerned" about the impact of events on all those involved.
Megan was reunited with her family at the weekend.
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The singer had been tweeting in support of migrants when she was bombarded with abusive messages.
Ministers are reportedly considering plans in a bid to lower inward migration.
In a tweet on Saturday, the US president didn't give a reason for his absence but said he wished"everyone well and have a great evening".