You seem to be under the misaprehension that the songhai empire survived to the scramble of africa.

It didn't. The songhai people did and they did fight the french, but the large empire you're thinking of had long since collapsed, destroyed by an invasion by Morocco.

But also the Songhai were never that powerful. They were a powerful state but they were not all conquering, they were defeated by the tiny vassal state of Kebbi due to their inability to muster a force capable of breaking the stone walls of the city. Which among other things shows how they weren't a gunpowder empire, they had no guns or cannons. And their control was largely nomial in a lot of areas and based around securing tribute rather than direct control.

Also while they were larger than mali or ghana, they were structurally unstable. Edward William Bovill wrote in the 1950s that the ruling dynasty was almost entirely unable to estalish a peaceful system of succession, that the songhai ethnic group were despised by most of the people they ruled and that there were deep divides between the islamic townspeople and the pagan farmers which meant islamic scholars viewed the songhai as only nominal muslims while the farmers viewed the songhai's support of islam as betrayal.

The morrocan conquest happened because their sultan al-mansur had heard that the songhai's internal divisions had meant the country had collapsed once more into civil war. In the aftermath of a long dynastic struggle, a petty quarrel between governors had led to a general revolt by the west against the central government, which meant the Songhai weren't strong enough to resist invasion or able to muster their entire forces.

Morocco sent only 4,000 men over the desert, but they were divided equally between infranty and cavarly, and armed with aquabuses and with six large cannons and several small ones. It was a much more formidable force than the army of the songhai, which was still spears and bowman at this stage.

The real problem was supplying an invasion over the sahara is incredibly difficult which is why more than twice as many men were sent simply to carry food and water as to fight and yet according to Mahmu al-kati it was still only 1,000 of that 4,000 strong army that even made it to the battlefield.

But because the sahara was so dificult to cross, the songhai army wasn't expecting any attacks from that direction, there were no fortifications or local regiments and so they couldn't deal with the invaders early on. By, for instance filling the wells so they could die of thirst, which they attempted to do but too late. Likewise, the full army couldn't be mustered until the moors had already arrived deep into songhai territory. The morrocan troops had great trouble passing rivers as they had no boats and would have been easy pickings if the army had caught them early enough.

Eventually the morrocans faced an army of 18,000 songhai troops at Tondbe. And the songhai were defeated there largely because they didn't know how to deal with gunpowder. Their soldiers broke under fire, as they'd never experienced it before, and their attempt to stampede cattle at the moroccans backfired when the cows panicked due to the sound of gunfire and headed back into the songhai lines.

The moroccan army sacked gao, their capital, (where they were largely welcomed warmly by an elite who'd never really liked the songhai rulers and wanted trade with morocco) and the entire empire collapsed.

It was too unstable to bounce back but also the morrocans couldn't hold power there from the other end of the sahara so the region fell into anarchy. The trade routes north had been disrupted and were somewhat replaced by traid routes going to south to the european ports on the guinea coast, so that the region was no longer so rich from the trans saharan trade and by the time 200 years later that the french turned up, there was no empire of that scale in the region to challenge them.

Sources: The golden trade of the moors, reviving the islamic caliphate in early modern morocco and medievel africa.