Question

What factor is most likely responsible for the spike in Europe's population that took place from about 1800 to 1950?

Answer 1

The high fertility rate on that continent during that period
mathematically produced a monotonically increasing population.

Although I'd hardly call a period of 150 years a "spike" .

Answer 2

The period during which Europe developed and developed a civilization and a great Renaissance era was at the same time and at all levels also increase in the rate of reproduction or fertility