Birth rate
According to the CIA's "The World Factbook", the country with the highest birth rate is Niger at 6.49 children born per woman and the country with the lowest birth rate is Taiwan, at 1.13 children born per woman.
Legitimacy (family law)
It is notable that traditionally-conservative Catholic countries in the EU now also have substantial proportions of nonmarital births, as of 2016 (except where otherwise stated): Portugal (52.8% ), Spain (45.9%), Austria (41.7%), Luxembourg (40.7%) Slovakia (40.2%), Ireland (36.5%), Malta (31.8%).
To a certain degree, religion (the religiosity of the population - see Religion in Europe) correlates with the proportion of nonmarital births (e.g., Greece, Cyprus, Croatia have a low percentage of births outside marriage), but this is not always the case: Portugal (52.8% in 2016) is among the most religious countries in Europe.