Jeremy Forrest, 30, will be arrested over the abduction of Megan Stammers if he is caught on the continent, Sussex Police confirmed.
"That is correct," a spokeswoman for the force in southeast England told AFP, adding that more details would be revealed in a press conference later on Thursday.
Forrest and Stammers left Britain on a ferry from Dover to Calais a week ago and have not been seen since.
Stammers is thought to have gone with Forrest voluntarily and police do not believe she is "at risk", but they are seeking to reunite her with her family.
Her parents have made an emotional plea for her to return, while police have appealed to her maths teacher to "do the right thing" and bring her home.
Forrest, who plays in a rock band under the stage name Jeremy Ayre and is married to a 31-year-old woman, had hinted at a "moral dilemma" on his blog
four months ago.
France has open borders with Spain, Germany, Italy, Belgium, Switzerland and Luxembourg under the Schengen Agreement, raising speculation that the pair may have moved on across the continent.
The age of sexual consent is 16 in Britain, but a relationship between Forrest and Stammers would not be against the law in France, where the age is 15.