It all depends on the combination of inflow - and the 'target sea level' of the flooded chotts. Once you have that, as long as you create a guiding trench to start the river going, and cut a gap through any inconvinient mountains, you can just go east. Much cheaper than the Atlas approach.
But going through the Atlas Mountains is just more work than is needed. Some way of getting water in from the east (be it desalination, or your canal), let the system stabilise and then add the outflow river.
The alternative to the salt problem is to build a giant drying pan. Dredging salt out of something built for an industrial scale COULD help with the salt levels. - but the better water in, the less of a problem in the first place.
It is notable the Eastern Mediterranean is saltier than the Western, because of the water flow. And the westernmost parts of this sea in Algeria would be below sea level and definitely be saltier. Thinking of it, if you establish the level tilapia and other hardy species of fish can thrive it (less salty than, say, the Great Salt Lake) as the target level of salinity, you have a nice target to keep thing at. With artificial rivers and salt harvesting, the target level should be met. And even after mass fish dieoffs in the Salton Sea in OTL, there were still fish there, so the issue of fishing isn't too hard to solve, and the chotts are an easier issue to solve than the Salton Sea for so many reasons.
But there's definitely a difference between the first two chotts and the other chotts. Would you turn the first two to freshwater, but let the others become saltwater (still taking effect of the climatic effects they would create)? Or vice-versa--the ones above sea level become extensions of the Mediterranean, but the ones below sea level become freshwater. Although I'm not convinced freshwater lakes can exist from the chotts, although useful saltwater "lakes" (more of an inland sea) certainly can. I'm thinking that for the westernmost chotts, the solution to prevent them from turning into hypersaline wrecks is to have enough water flowing into them.
Outside of the initial cut which floods the chotts, the only outlets are through what's basically Star Wars's Dune Sea (nice way to butterfly Tatooine as we know it), the Atlas Mountains, or a cut which would pass near the modern city of Gafsa in Tunisia.
And then of course, is this something which 19th century people might consider?