Sahel has a bigger problem, politically speaking, with a very low level of integration of the population in these nations. If you can call them nations. There are different ethnic and religious groups (and religion can be like a form of ethnicity). In this case, the expansion of conflict has been driven primarily by Arabs, Tuaregs and Fulani. But in Mali, the junta's power base is in the Bambara. Burkina Faso, the Mossi. In Niger, the Zerma. It's more complicated and other people support the juntas, and then the Tuaregs have their own movement while the Islamists have been heavily recruiting Fulani.
Jihadism BTW is not an ethnic ideology. It crosses borders and lines for the struggle for the sake of God.
Then you add that these regimes have a very weak grip over their own territory. Vast stretches of the countryside are bandit zones. Then you add rapid increase of the population and ensuing social problems over resources and grazing rights between semi-nomadic herders and townspeople. These countries are much less developed than even, say, Senegal or Cote d'Ivoire. The Sahel was much less "colonized" (ironic for those who blame colonialism). Liberal influence (with a French accent) mostly came from the outside through hamfisted U.N. and NGO programs. But that always looked sus to people.
So like Algeria, there was an attempt to democratize things in the 90s, but it didn't work, and the military would repeatedly step in. The more recent round is more serious and has taken on more ideological language. A highly successful narrative took hold that the West (mainly France) was to blame for their problems. But the average Malian guy would see chaos and also French troops rolling around, and wouldn't understand it. There's chaos... and French... and uhhh. So the military guys, when they made their move (helped by hysterical Russian propaganda blasting videos to that guy on his phone), would just say "the French are behind it, so give us all the power."