I can see why they wanted more than just 1 Vulcain on the core: because they wanted the core to be able to "fly alone". As you said - one 100 tons thrust Vulcain can't lift a 160 tons EPC.
So they added Vulcains engines, only to realize they could dropping them Atlas style.
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Applying Ariane 4 taxonomy to Ariane 5: Ariane 50 would not work.
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Ariane 52P would be the baseline: 100 tons thrust Vulcain plus PAP x 2 = 140 tons of additional thrust.
So
Ariane 52P + Aestus
Ariane 52P + HM-7 and eventually
Ariane 52P + Vinci
Rinse, repeat with Ariane 53P (three solids, 120 degrees apart on the core) and Ariane 54P (four solids, 90 degrees apart)
Of course if you wanted PALs rather than PAPs, Viking is still out there (even today) : in India. But storable propellants are out of fashion.
Personally there are a few points that I could see becoming problem with that CNES A5C proposal
-Designing such a modular launcher will have restrictive requirements, especially on the first stage, that will have to handle very different loads across versions, when considering the fact that it won't be "hanging" like Ariane 5, it's likely that the H160 will be significantly heavier than the EPC of Ariane 5 (looking at DIVH or CZ-5 core, both designed to be modular and handling higher thrust, we may be looking at 1.5-2x higher dry mass), which will really impact performances of the smaller versions. Your proposal definitely helps there, although maybe limiting to A52 and A54 may be structurally and logistically easier.
-Ariane never had very high launch rate, and it's likely that some of these upper stages configuration would only fly occasionally in intermitent production batches, we saw with Ariane 5 that keeping production lines of non-ECA variants were not worth it (sadly, those A5 ES would have been useful these past 2 years...) . It may be a better idea to only have a single intermediary upper stage instead of two hydrolox ones+an hypergolic one. IMO that's where the limit of the HM7 appear and something like vinci is needed.
-If it does have a higher launch rate than Ariane 5, probably more comparable to Ariane 4's or the planned Ariane 6 (...) launch rate, which a modular launcher needs to fully take advantage of it, there is IMO serious doubt that the indsutrial chain could, at the time, produce Ariane 5-sized EPC/H160 at an A4 or planned A6 cadence, the planned A6 cadences depends on a bunch of choices (no/less milling for the tank panels, friction stir wielding, no common bulkheads, simpler and partially 3D priinted Vulcain 2.1...) that simply weren't available or don't seem chosen for this "Ariane 5C"
As for viking - sad that it was considered out of fashion, elsewhere it's still going strong.
-ISRO about to launch its first astronauts on a Vikas powered LVM3 in 2 years
-ISRO also developping a Throttleable, Restartable reusable Vikas for a New Shepard-like suborbital tourism launcher for the 2030s
-CASC announcing that they're still going to be launching the (Ariane 4 inspired) Long March 3B into the 2030s...
Looking at the Vikas, it's clear that there was still margin for improvement of the Viking.