You cannot have your cake and eat it.
For simplicity, I'm assuming that the 'attack roll' from Cloud Rune is sufficient to hit any creature, and thus treating 'attack roll' as synonymous with 'attack'. I will use 'wizard' to signify the Fire Shield caster, and 'goblin' to signify the new target from Cloud Rune
1. The attack has only one target
The chosen creature becomes the target of the attack
'Becomes the target' denotes substitution, rather than addition; there is one target - 'the target' - and the thing which changes is the identity of the target, rather than the number of targets.
The wizard casting Fire Shield can be the target of the attack, or the goblin targeted by Cloud Rune can be the target. They cannot both be 'the target' of the attack. This should be obvious, because the whole point of Cloud Rune is that the original target is spared the effects of the attack.
2. Cloud Rune transfers all the effects of the attack
The chosen creature becomes the target of the attack, using the same roll. This magic can transfer the attack's effects...
There is no case here for a division between 'being hit by an attack' and 'taking damage from an attack'. Cloud Rune does not transfer attack damage; it transfers the entire attack and all of its effects.
Only one target creature is hit by the attack, and that creature suffers the attack's effects. No other creatures:
- Can be considered the target of the attack
- Are effected by the attacks effects
3. One of the 'attack's effects' is the opportunity to trigger certain reactions
Imagine our goblin also has a reaction which is triggered when she's hit by an attack - the Shield spell, for instance. Because Cloud Rune has been used to make her the target of the attack, she may use her reaction to cast Shield. As the attack's target, that's her sole prerogative. The wizard cannot use a reaction to cast Fire Shield, because the wizard was not targeted by an attack; There is one attack, and the goblin is its only target.
To put it in concrete terms: If you're going to deal damage with Fire Shield, you must take the damage* from the triggering attack. These are both consequences of being the attack's target, and you can't have one without the other.
Guiding principle: Reactions must result in consistent realities
Many reactions appear to tamper with reality. Shield, for example, cancels its own trigger. This is fine, because the purpose of the spell is to substitute the triggering reality for the desired one. In one reality, the triggering attack hits. In another reality, the triggering attack misses. Both realities are coherent within themselves.
In this questioner's example, a paradoxical, inconsistent reality is being created. The wizard is hit by an attack and triggers Fire Shield. Cloud Rune is cast, making the goblin the target of the attack. The wizard is no longer the target of the attack, so the wizard cannot possibly have cast Fire Shield in response to being that attack's target. You cannot have your cake and eat it.
* Except in the case of exceptions. It is obviously possible to be hit by an attack and take no damage from it.