Magistrates in Bordeaux granted the request during a short hearing this morning.
Forrest, 30, did not appear in court and was represented by his lawyer Daniel Lalanne.
The maths teacher from Ringmer, East Sussex, disappeared with a 15-year-old pupil on September 20 and was arrested in the south-western French city on Friday.
It followed the issue of a European arrest warrant after the pair failed to use their return Dover-Calais ferry tickets.
Mr Lalanne said after the hearing he did not know when Forrest would return to the UK but that it could be "at any moment".