Hmm, trying to win with geography details?

Look, "vast desert region" communicates to me a difficulty to exercise control and to find the opposition. That's not leading to what's really relevant there imo.

No matter what hold the government's opponents have on isolated settlements; the country is really about the Niger river and its green belt.
An intervention force would hardly focus on some outlier settlements - even if they are epicentres of the opposition - and meanwhile ignore the green belt where most of the population under 'control' of the opposition lives at.
An intervention force would hardly have the manpower to occupy much with 3,000 men (likely less than 50% teeth) and the government of Mali is no doubt more interested in high-pay-off control of Niger green belt settlements than in low pay-off occupation of unfriendly outlier settlements.

So yes, I expect that intervention forces would focus on driving the opposition forces out at the Niger river, possibly with two hook movements to set up checkpoints against fleeing opposition forces.
I doubt that they would go for lesser settlements first, and I even doubt that foreigners would attempt to solve this fundamental conflict themselves or to suppress it in the long term.
The French are more known for assistance or raid-like missions (even outright punitive expeditions as in Cote d'Ivoire and with the bombing of a Libyan airbase in the 80's). To rout the opposition forces along the river would fit into their pattern imo.


This whole "vast desert region" thing reminded me a lot about the talk of "battle-hardened Iraqi desert army" in 1990, when even a superficial look at maps showed that the Iraqi army had "fought" for eight years in hills, swamps and little desert.