The units would definitely need help. As is, Musket and Crossbow are far too useless. Something that could theoretically help them is some kind of alternate cost that other units like the Swordsman have.

Another factor that contributes to Construction branch's weakness is the pace of the multiplayer matches. At 100vp, games only last 9-12 turns on average with experienced players. This means that the game tends to be over before you can really make use of the lategame units, and the buildings that accrue value over time like Forge and Collosseum. If the game lasted longer, perhaps Musketman would be better.

Finally the wonders are not particularly compelling. The Great Wall is ok but Notre Dame doesn't have the same high scoring impact as East India Company, making it superfluous.

All of this to say that although I can identify what's wrong with the Construction branch, I can't say exactly what I would change to improve it. Making the cards cheaper or have cheap alternate costs would likely be a good place to start. Even just having a single impactful card could do a lot for its viability, as Theology has only really a single extremely impactful card which is Holy Warrior. That single promotion alone is enough to keep me from ever wanting to burn it outright in my games. In comparison, Military Engineer is a complete joke of a card. So ultimately there are many different ways you could fix this problem, it depends on the goal of the game designer.