Paris prosecutors must now decide whether to pursue the matter further but, with no charges made when the investigative magistrates filed their report on 20 December, the case could well be dropped.
But anti-child prostitution NGO Ecpat, which filed a legal complaint relating to the case, said Wednesday it may appeal for further inquiries to be made, as it has the right to do during the next three months.
Two other investigations into allegations of sexual abuse by French troops in the CAR were opened at the same time.
One was closed in November when the girl concerned changed her story but the other, into allegations of statutory rape of three children in Dékoa in the centre of the country, is still under way.
Sangaris troops protected from prosecution in CAR
France launched the Sangaris operation in December 2013 at the request of then-president François Bozizé when Muslim Seleka rebels were advancing on the capital, Bangui, and sectarian violence exploded between them and Christian anti-balaka militias.
The CAR government agreed that any French servicemen accused of crimes in the country would be judged by French judicial authorities.
Three French examining magistrates opened an investigation in May 2015 into allegations of rape in a refugee camp near the Bangui airport between December 2013 and June 2014.
Fourteen French soldiers were named in the beginning.
The investigators went to CAR in July 2015 and in the summer of 2016, interviewing about 10 children.
The affair was kept under wraps until the UK's Guardian newspaper published a leaked UN memo alleging child sexual abuse in the CAR.
It claimed that children had been persuaded to perform sexual acts in exchange for food or small amounts of money.
A UN inquiry has named 41 Gabonese and Burundian suspected of sex crimes in Kemo, in the centre of the country.
Lack of resources for inquiry alleged
French Defence Minister Jean-Yves Le Drian said he would be "implacable" if any French soldiers were found guilty but the Mediapart website has accused the authorities of not matching words with action.
Journalists Justine Brabant and Leila Minano have interviewed alleged victims in Bangui and other parts of the country, as well as investigators and soldiers involved in Sangaris.
They have collected accounts of prostitution, rape and oral sex in exchange for food or money, often with minors.
Several officers warned that the military camp in Bangui was "like a Swiss cheese", allowing free access to a prostitution ring, the site says.
But the military's reaction was to cast doubt on children's testimony and on the ethics of NGO's who supported the witnesses.
Military investigators, who intervened before the civilian magistrates, waited five months before visiting Boda to interview one witness, pleading that no helicopters were available to fly them in, Mediapart reports.
Although she said her son was the child of a French soldier, they failed to carry out DNA tests, simply asking what the child's blood group was, the journalists say.
At another camp, in Mpoko, they described children's testimony as "unlikely" and "lies", despite one of them recognising the photo of the alleged abuser and the discovery of child pornography on one of the soldiers' computer.
Ministry says soldiers disciplined
"The Defence Ministry seems to admit that rape or sexual abuse have been committed by French soldiers in CAR," Mediapart comments.
Replying to an email of 20 December 2016, the ministry said that "every time the accusations are proved and the authors identified" the "soldiers in question" have been moved away from the theatre of operations and have been disciplined.
But a request to give details of how many such cases there have been has been left unanswered.