Caveat - Shapechange is a concentration spell
While you do say that you assume concentration is maintained, this appears to be a reference to the fact that the druid does not go unconscious when they fall to 0hp because they revert to some form with positive hp.
I note as a caveat to what follows that for the druid to be reduced to 0hp, they likely took damage, and would thus likely have been making Concentration saves before they were reduced to 0hp. The druid class does not get their proficiency bonus on Constitution saves, and the druid will be using the Constitution score of whatever form they are in when they take the damage. Thus, barring complicating shenanigans1, it is possible they will be forced out of their shapechange before they are forced out of their wild shape and before they are reduced to 0hp.
A whole lot of DM decisions
Wild shape tells you that it ends when you are at 0hp:
You automatically revert if you fall unconscious, drop to 0 hit points, or die.
Interestingly, Shapechange does not say this explicitly. It does say (as wild shape also does):
When you revert to your normal form, you return to the number of hit points you had before you transformed...
If you revert as a result of dropping to 0 hit points, any excess damage carries over to your normal form.
But unlike wild shape, it doesn't actually say that you do revert as a result of dropping to 0hp. Let's assume that Shapechange has this clause, at least implicitly.
What is your normal form?
Ending either of these conditions reverts you to your "normal form".
But what is your normal form? Is it your true form2, that of the druid, which might draw on the standard English meaning of normal as "usual" or "typical"? Or is your normal form the form you had at the moment you transformed to new form, which could use the standard English meaning of normal as "conforming to a standard"? Wild shape was likely written with language that assumed it was your only transformation, but shapechange has to contemplate that you might be transforming multiple times while under its effects. It thus uses a welter of terms: normal form, original form (which is not the caster's true form but rather the form they assume in their first transformation), different form, and new form. Within the context of the spell itself, it seems clear that "normal form" means the druid. However, even shapechange likely doesn't suppose that you might be in wild shape when you cast it. Thus, in the absence of a definition for "normal form"2, it is unclear whether "normal form" is unambiguously the druid's true form, or whether it could mean 'the form the druid was in when they cast the shapechange spell'. So you need a DM decision here whether 'normal' in this context means 'true' or 'at the time of casting'. Similarly, "normal form" for wild shape could mean 'form at the time wild shape was used'. If ending either effect returns you to your true form regardless, then it doesn't matter which effect is ended or when.
Will reaching 0hp trigger both end conditions?
It is possible that since both effects have had their end conditions triggered, they are both ended, in some order that need not be determined. If both effects are ended, then you will return to your druid form regardless.
But if the end of the second transformation returns you to the form of the first transformation, and if that form has positive hp even after damage carryover, then perhaps the 0hp-trigger that would have ended that transformation 'checks again' and fails before ending the first transformation.
The question is do triggered effects check to see whether they still have valid targets before they resolve? In M:TG, for example, they do check (Rule 608.2b): if multiple triggers are 'on the stack', the resolution of one of them might make the target invalid for a later resolving one, in which case it would not resolve.
As far as I can tell, D&D 5e doesn't have any explicit rules to guide us about such events. We don't even have clear rules on whether an ongoing spell is ended, suppressed, or unaffected when its target is no longer valid. Thus the DM needs to decide whether they want triggered effects to check whether a target is still valid before they resolve. If they don't, then the order of resolution of these two effects doesn't matter. But if the effects do indeed check their target, then the order they are resolved does very much matter - even though there are no official rules about the order in which to resolve them.
If only one of the transformation effects ends, and if ending one of the transformation effects reverts you to your previous form, the one you had before that transformation, then it might matter which one ends first, since ending the first transformation would revert you to your true form and at least in effect cancel the second transformation, but ending the second transformation would revert you to the first transformation, not your true form.
Suppose you hit 0hp, which triggers the end conditions of both effects, the spell and the class feature.
Which effect will end first? This is a simultaneous trigger problem, where there is not an official rule but there are at least some well-defined options. You have three choices. You can resolve them as decided by the player whose turn it is (an optional rule from XGtE), you can decide them in Initiative Order (an unofficial ruling suggested by a JC tweet), or you can decide them by DM fiat (Rules 0, 1, and 3) - which might include the ruling that the currently-worn form is the one that is ended first.
Conclusion: the DM has some decisions to make
To answer your question, the DM first will need to decide what is the druid's 'normal form'. They may then also need to decide whether the end condition that is resolved second will 'check again' and then not implement if the druid does not have 0hp after the resolution of the first. Finally, if trigger resolution order actually matters, then they will need to decide how to resolve the trigger order, and can choose between DM fiat, an optional rule, or Initiative order.
The following table might help - the DM should start in the first row and stop there if they agree with that assumption. If they don't agree, they should proceed to the next row down, and so forth.
||Druid Reverts to
|'Normal form' is the same as 'true form'
||Their true form
|'Normal form' means 'form at the time the spell was cast or ability was used', but 0hp trigger ends both transformations
||Their true form
|'Normal form' means 'form at the time the spell was cast or ability was used', 0hp triggers the end of both transformations but after one transformation is ended the other trigger checks hp again and is not ended, and the transformation ended first is the first transformation
||Their true form
|'Normal form' means 'form at the time the spell was cast or ability was used', 0hp triggers the end of both transformations but after one transformation is ended the other trigger checks hp again and is not ended, and the transformation ended first is the second transformation
||The form of the first transformation
1War Caster feat, Bear's Endurance, etc. Also note that while wild shaping first and then casting shapechange requires a 20th level druid, shapechanging first and then using wild shape can be done by a druid of 17th level, which gives you three levels of multiclass possibilities, including starting as a class which does have proficiency on Constitution saves.
2"True form" and "normal form" are not defined game terms. "True form" is by far the preferred term in the Monster Manual, where it is used for 32 creatures, many but not all of them shapechangers. In contrast, only the Mummy Lord "reverts to its normal form" after a transformation. The PHB, on the other hand, favors "normal form", and uses it for the wild shape class feature as well as in the spell descriptions of animal shapes, lightning arrow, polymorph, shapechange, and true polymorph. The PHB does use "true form" for the class feature turn the faithless, though, as well as the spells witch sight and mirage arcane.