1. Wanting to stop it.
This desire is absent. Policy is therefore irrelevant.
2. So, the question becomes something like - Why are Europeans indifferent to demographic decline?
3. Why don't European's regard having children as a major priority?
4. Why don't European's regard permanent marriage and family as the major priority?
This is getting a bit closer...
Individuals... Why would an individual European person put marriage and family as priority? Clearly it must Not be as a short term reliable route to maximise happiness...
So it's about the long term and the cosmic and supra-individual... We are talking about Religion.
5. The answer to what would stop Europe's demographic decline is Religion; serious and as a priority...
6. The next question is what kind of religion?
But at least we are clearer about the nature of the right answer.