Burkina Faso claims it wants to defend itself since it fights a jihadist insurgency at the moment.
Currently stationed in Burkina Faso are 400 French special soldiers, who have one month to leave.
France also withdrew neighbouring Mali last year after eight years of fighting jihadist extremists there.
In West Africa, France has maintained strong military relations with many of its former colonies and has assisted a number of countries in battling jihadists operating there as part of the now-defunct Operation Barkhane.
However, because to its ongoing economic ties, Russia has been able to capitalize on some resentment of its involvement.
Currently, Wagner, a Russian mercenary force, is cooperating with both Mali and the Central African Republic.
Burkina Faso has dismissed suggestions that it will work with the Wagner Group to combat the jihadists, but an AFP story claims that a liaison team from the mercenaries has already visited.
A representative of the French foreign ministry acknowledged that the Burkinabe administration had made a formal request for its troops to go.
The spokeswoman declared, "We will honour this request in accordance with the conditions of the Agreement."
An insurrection that has lasted ten years in Burkina Faso has driven over two million people from their homes.
Most recently, alleged jihadists abducted some 60 women who were gathering food in the country's north, and at the beginning of the month, the bodies of 28 persons who had been shot dead were discovered in the northwest.
