The woman, who is a legal resident of the United States, did not have valid documents to enter France, where she had previously applied for asylum.
She was scheduled to be on a flight to the U.S. on Saturday afternoon but French authorities removed her from the aircraft after she started screaming, according to an official.
"We are going to try to send her back again with a French escort," the official said.
The woman was expected to be accompanied by six US marshals on Tuesday's flight back to New York, authorities said.
Then, she was due to leave France on a flight at 2:30 p.m. local time (8:30 a.m. ET) Tuesday, a Paris airport official told CNN.
She was onboard the plane when Delta refused to fly her, a Paris airport official has told CNN.
She was taken off the flight and put back into police custody and will remain in France temporarily.
The 57-year-old woman got past multiple security checkpoints at New York's John F. Kennedy International Airport and boarded a plane to Paris last week.
Delta Flight 264 took off from JFK Airport and landed at Charles de Gaulle Airport in Paris the next day with the stowaway, authorities said.
New video shows personnel attempting to restrain the unruly passenger on November 30.
In the video the woman can be heard saying she does not want to return to the United States, that she has "asylum against the United States," and mentioning the Geneva Conventions.
"She kept on saying 'I do not want to go back to the USA. Only a judge can make me go back to the USA,'" said Gary Treichler, who was on the flight with his family.
Police boarded the plane at the Paris airport, according to a video from a passenger that was shared on social media. "This is the captain. We're just waiting for the police to come on board," the pilot can be heard saying.
Daniel Velez, a spokesperson for the Transportation Security Administration, said "an individual without a boarding pass" was screened at Kennedy and was not carrying any prohibited items.
"TSA takes any incidents that occur at any of our checkpoints nationwide seriously," Velez said. "TSA will independently review the circumstances of this incident at our travel document checker station at JFK."
The French National Police said Friday, "A passenger of Russian nationality was smuggled onto a flight from NY (JFK) to Roissy-Charles de Gaulle."
The passenger "was refused entry to France for lack of a valid travel document (visa), and was placed in a waiting area for the time needed to return her to the United States as she held a valid US residence permit," the National Police said in a statement.
A Delta spokesperson said in a statement, "Nothing is of greater importance than matters of safety and security. That's why Delta is conducting an exhaustive investigation of what may have occurred and will work collaboratively with other aviation stakeholders and law enforcement to that end."
A spokesperson for the Port Authority of New York and New Jersey, which operates Kennedy Airport, declined to comment.
Federal investigators are looking into how the woman breached several security points at JFK and slipped onto the plane without a boarding pass.
Inspectors from TSA are also preparing a civil case against the stowaway after reviewing airport security video from inside John F. Kennedy International Airport, agency spokesperson Alexa Lopez told CNN.
"The TSA will open civil cases against passengers when there's evidence that procedures may have been violated," Lopez said. The TSA cannot bring criminal charges, though it can refer them to the Justice Department.
Delta has not said how the woman was able to board the plane once she made it past the TSA checkpoint.
CNN contributed to this report.