He said the French judicial authorities wanted to talk to "the person held in Florida" and to follow up investigations concerning him, but refused to publicly name Montez.
French prosecutors said tests showed DNA from Spaniard Francisco Montez had "very important similarities" to samples found at the youth hostel in France where the 13-year-old was killed in 1996.
But assistant public prosecutor Yves Boiven, speaking in Rennes at 2100 BST, did not confirm the DNA was an exact match.
He said the French judicial authorities wanted to talk to "the person held in Florida" and to follow up investigations concerning him, but refused to publicly name Montez.
Mr Montez, 51, could only be sent to France if French authorities request his extradition from the US, but M Boiven refused to say whether this request would be made or to speculate on how long it might take.
Speaking shortly after the French statement, Caroline's father John Dickinson, said: "After five years of searching it looks as if we have been able to make progress.
"Nothing can bring back our dear Caroline, but everything should be done to prevent such a nightmare being visited on another innocent family."
He added the family had never given up hope that Caroline's murderer would be found.
Testing differences
French detectives brought the samples back from the United States earlier on Saturday.
In Florida, where the suspect is being held, police said they were "99.9% certain" that DNA tests on Mr Montez would link him to the murder.
However, French officials wanted to examine the samples in France because of differences between US and French testing processes.
Caroline, 13, from Launceston in Cornwall, was attacked on a school trip in France in 1996 while she was staying in a youth hostel dormitory.
Alert USA officer
Mr Montez, who is from Asturias in Spain, was arrested on 11 March in Miami Beach after allegedly breaking into a woman's apartment and attempting a "lewd and lascivious act" while she slept.
Last month a French court named him as a chief suspect in the Dickinson case, and as one who was "particularly" wanted by police from a list of about 50 people sought for questioning.
But the US authorities only realised his possible link with the Dickinson case because US immigration officer Tommy Ontko had read about the schoolgirl's murder while on holiday in Britain.
Mr Dickinson praised Mr Ontko for his vigilance, saying: "I would like to shake his hand."
Last week an inquest ruled that Caroline's death was the result of unlawful killing.
The inquest had heard that two girls in the same dormitory were disturbed by noises coming from Caroline's bed but went back to sleep thinking she was having a bad dream.
Her lifeless body was discovered the next morning.
French police have so far taken more than 3,500 DNA samples from men in France and Britain in a bid to track down her killer.
Mr Boiven said: "Until today, none of these tests gave any significant similarities with the genetic traces taken from the scene of the crime."