Real Madrid striker Benzema and Bayern Munich forward Ribery, who are not attending the four-day trial, are being tried on charges of paying Zahia Dehar, a prostitute-turned-fashion model, for sex in 2008 and 2009, when she was aged 16 and 17.
Ribery has admitted paying her for sex but said he did not know how old she was. Benzema has denied having any sexual relations with Dehar.
Paying for sex is not illegal in France but underage prostitution is.
The trial is going on amid a heated debate in France over a reform of prostitution laws aimed at imposing fines on clients.
Benzema and Ribery's lawyers said on Monday they are confident the players would be cleared of all charges.
They stressed that a Paris prosecutor said during the investigation that there is no evidence to prove that Ribery and Benzema could have known the girl was a minor.
"The prosecutor has asked for the case to be dismissed," Carlo-Alberto Brusa, Ribery's lawyer, told reporters at the Paris court where the trial opened.
"(Dehar) is not a civil party in the case anymore. She does not see herself as a victim, so we have a trial but no accusation," he added.
Image: Karim Benzema (right) and Franck Ribery.
Photograph: Phil Cole/Getty Images
PHOTOS: Ronaldo, Pele get emotional at Ballon d'Or awards night
Ronaldo wins World Player of the Year for second time
La Liga: 'BBC' trio lead Real Madrid to 5-0 romp at Betis
Ronaldo must continue to maintain his exceptional standards: Pele
King's Cup: Ronaldo on target as Real knock out Osasuna