According to Article 40 of the Constitution:

Article 40 [Interim Presidency]

(1) In the case of a vacancy or an incapacity declared to be absolute by the Constitutional Council, the President of the Senate shall become the interim President of the Republic for managing current business. The Prime Minister and the members of the government considered as having resigned, shall assure the managing of current business. The interim President may not discharge them from their functions. He may not have recourse to the people through a referendum nor dissolve the National Assembly.
(2) Unless a case of force majeure is declared by the
Constitutional Council, the election of the new President of the Republic will take place within three months from the declaration of vacancy or absolute incapacity.
(3) During the interim period, no constitutional modifications may be instituted either by referendum or by parliamentary means.

So, there is a constitutional out from the current crisis if the military agrees to return to the barracks and to reinstate the president.  The international community should keep this in mind as policy makers determine how to handle the situation.