Lawyers for Ramadan had requested his release last month after unsuccessfully trying to have the charges dropped over discrepancies in testimony given by one of the women.
Ramadan, who took leave from his post at Oxford University after the allegations surfaced, has also complained that his imprisonment has made it more difficult for him to receive treatment for multiple sclerosis.
But the appeals court upheld his detention on Wednesday, considering Ramadan, who holds Swiss citizenship, is a flight risk despite his offer to surrender his passport and post 300,000 euros ($350,000) in bail.
Investigative magistrates had already denied several requests for his release.
Ramadan, whose grandfather founded Egypt's Muslim Brotherhood movement, has been held since February on charges that he raped two women in France in two separate incidents.
His accusers came forward in October in the wake of the “Me Too” campaign which began after several women accused Hollywood mogul Harvey Weinstein of sexual assault, prompting women worldwide to share accounts about sexual attack and harassment.
Ramadan, a married father of four who is one of European Islam's best-known figures, has denied any sexual relations with the two women, saying he met with each of them only once and in public places.
He has denounced the accusations as part of a smear campaign by his critics.
His first accuser, Henda Ayari, who was questioned by judges last month in Ramadan's presence, had originally said that he raped her at the Crowne Plaza hotel in Paris on May 26, 2012.
But investigators later determined she was attending her brother-in-law's wedding that day in Rouen, northern France.
Ayari subsequently admitted she could not remember the exact date.
On September 18, Ramadan will be questioned in the presence of his second accuser, a disabled woman identified as “Christelle” who claims he raped and beat her in a hotel in the southeastern city of Lyon in 2009.
French investigators are also looking into rape claims made by a third woman with whom he has admitted to having had an affair.
Those allegations have not yet let to charges.
In Switzerland, a Swiss woman has also filed a complaint against Ramadan.