He would've ended up governing like his friend Jerry Rawlings in Ghana during the 90s, or he would've refused to do so and ended up killed/overthrown by another coup done by a different officer than Compaoré. I'm pretty certain he had no way out besides either his own death or compromise of his original ideals. And I say this as someone deeply intrigued by Sankara and his ideals.
This is what I said about Sankara on azander12's thread:
Sankara reminds me a lot of Robespierre - a honest, modest man whose concern for the well-being of his country and people is real, but for whom the end justifies the means. Any means; up to and including a campaign of terror and the establishment of an authoritarian regime bordering on totalitarian.
azander12 then compared him to the
Well-Intentioned Extremist trope; in our TL, he was more "Well-Intentioned" than "Extremist" but, if he'd lived longer, I think he would've had no choice but to turn the authoritarianism up to 11, in order to stay in power and defend his ideals, his regime and himself from the many,
many enemies he would've collected, both inside and outside Burkina Faso.
He was born in 1949, so there's a chance he'd be alive today if he hadn't been killed; a Burkina Faso with a 67 year old Thomas Sankara in charge would've probably resembled Cuba in many,
many ways. A country punching well above its weight in some areas, but an authoritarian, poor country nonetheless.