Forrest, 30, and his teenage lover eloped to France in September. After a week on the run, they were arrested in Bordeaux.
The girl was flown home while Forrest was detained by the French authorities.
He was extradited in October under a European arrest warrant issued on suspicion of child abduction and has since been detained in custody awaiting trial.
British authorities want to add having sex with a minor to the abduction charge. But because the statutory rape charge was not included on the extradition request, they can only do so with the agreement of the French court that approved his handover.
The change in the charges would increase the maximum sentence Forrest could face from seven to 14 years.
State prosecutors have recommended accepting the British request but Forrest's lawyers have argued for it to be rejected in light of what they described as the legally unjustified treatment their client had received since being returned to Britain.
Forrest's lawyers also challenged the substance of the charges the British authorities want to bring.
That issue is complicated by the different ages of consent in the two countries.
A 15-year-old in France is judged capable of consenting to sex while in Britain she is still considered a minor. Both countries outlaw sexual relations between teachers and students in their care.