Interesting to see that the Romans are going south. I would have thought they were trying to get more of the Frankish lands. With the franks under pressure by the Saxons it would make sense. But I guess southern lands are more promising to the Romans
There's a couple of reasons for the Romans to try the Southern approach, emphasis on TRY, because they haven't won the war yet!:
1. Syagrius's regime is dominated by a tension between what we might think of as Northerners/Easterners, and Southerners. The former care a lot about the Franks, but the latter are far more concerned with the Visigoths. The successful war on the Somme has placated the Northerners, but the Southerners are only cautiously supportive and would balk at supporting deeper action into Frankish territory.
2. The South is more promising territory to gain in three key ways: it is more economically productive, contains more functional Roman cities, and in general expanding there would be a major economic gain for Syagrius. Additionally, Roman land-owning society is largely intact in the South and Roman warlords are common. In other words it would be relatively easy for Syagrius to establish and solidify administration of these regions. And from a strategic perspective, an expansion to the South does not expose his regime to new threats. IF the gains against the Visigoths are meager, and King Euric retains lands in Gaul, the Romans will still have the same set of neighbors to the South, just on more favorable terms. If they push the Visigoths into Spain, then they'll have an ally to the East (the Burgundians), the sea to the South, and the Visigoths again to the Southwest. A favorable outcome relatively speaking.
3. On the other hand, there are a lot of factors to advertise against Northern expansion. The Frankish lands are not particularly economically productive (aside from the Rhineland, but more about that below). Roman cities and the Roman way of life is already severely shriveled by this point. There is no significant reservoir of still-powerful Roman landowners or military leaders to call upon. The Rhineland is rich but not capable of defending itself. Indeed given the resources that Syagrius has, defending the Somme is a much better position than trying to hold the lower Rhine, or whatever intermediary position he might seek in the Frankish territories.
4. A weak and divided Franks is really the most favorable outcome for the Romans right now. The Saxons are flexing their might and the Alemanni would love a chance to fight some Romans. If the Romans took over Frankish lands, they've have to deal with these forces directly at significant threat.
Of course, if the Romans can make significant gains against the Visigoths, it would definitely shift their resource constraint considerably and change all these calculations
IF.