Not really sure how you can call it underpopulation. Was underpopulation also a problem in the preceding 30,000 years or so of human civilization in Europe leading up to today, when the population has always been always smaller?

The population in Europe is larger than it has ever been in any point in history.

Not under-population, per se, but low rates of growth.

Low rates of growth lead to a population collapse in 2 generations or so and an inverted demographic pyramid where mostly old people exist with few youngsters. Not a good recipe for the species or a civilization.

Look at predicted population numbers in Japan for example.

I'm unsure how low rates of growth in Europe will lead to a collapse of the species.