The decision will come as a huge relief to the Burkinabe, which is already without injured striker Alain Traore for Sunday's final.
CNN: Burkina Faso given Pitroipa boost for Sunday's AFCON final
It is due to host talks between the Islamists, Tuareg rebels and the Malian government in the Burkinabe capital, Ouagadougou, on Friday.
However, Burkinabe should not worry that the French double act will bankrupt their country's football: "both men agreed to financial concessions, " said President Diakite.
According to the Burkinabe football federation, Rabier will be given a further seven months extension to his contract if the team qualifies for Tunisia.
The Burkinabe have been boosted by the rescinding of Jonathan Pitroipa's sending-off against Ghana, with officials admitting he should not have received a second booking.
The French duo replace Jacques Yameogo and Pihouri Weboanga, who were the Burkinabe coaching duo fired after the Nations Cup in Mali earlier this year.
Many Burkinabe would rather not know whether they carry the virus.
The Burkinabe are also hopeful that Pitroipa will have his suspension overturned, although that depends on whether Jdidi admits to the error in his match report.
The victory gives Burkinabe six points in the group, and takes them above South Africa, who also have six points, on the number of goals scored.
But the Burkinabe will now go into Sunday's final at Soweto's Soccer City dreaming of pulling off a triumph with Pitroipa ready to lead from the front.
CNN: Burkina Faso given Pitroipa boost for Sunday's AFCON final
The Chelsea frontman did test Diakite in the 85th minute but the Burkinabe goalkeeper was equal to his snap-shot from a tight angle as the Ivorians' frustration continued.
Vahid Halilhodzic's team dominated possession but could not find the cutting edge to break down a determined Burkinabe defence despite a frontline of Didier Drogba, Bakari Kone and Gervinho.
It will be also the opportunity to revisit the thought of the Burkinabe Professor, especially his views on culture, education, endogenous development, Pan Africanism and youth, and to underscore their topicality.
However, Sengalese and Burkinabe officials denied the claims.
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