While there is no recent pre-compiled source that fully answers your question, we have compiled and triangulated the following from the available public sources: 18.8% of Europeans consider themselves non-professional cyclists, up from 17% in 2005. This includes 13.8% of Germans over the age of 14, 10.3% of adults in Spain, 13.3% in France, and 13.9% of adults in the UK.
Based on the research criteria, we understand "non-professional cyclist" to not refer to the number of Europeans who regularly use a bicycle as a mode of transport (e.g., to work), but those who ride for leisure, either in amateur cyclist events or on their own. Due to the paucity of recent data (24 months or younger), we were forced to rely on older material for much of our information. We will identify these sources in our deep dive below.
EUROPEAN AMATEUR CYCLING
According to a 2005 study, 17% of the population of the European Union members states age 15 and above participated in recreational cycling. However, the actual participation varies heavily by country: "Cycling is by far the most practiced physical activity in the Netherlands (53%), whereas only 2% and 3% participate in the sport in Greece and Portugal respectively."
Due to the age of the above source, we will attempt to corroborate it with a triangulation: A more recent source shows that there are 16.5 million bikes owned in the Netherlands (covering 99.1% of the population), with 1.3 million sold each year. This gives each bike an average lifespan of 12.7 years (16.5 / 1.3). In Europe as a whole, there were 263.8 million bikes sold in the 13 years between 2004 and 2016. Since the population of Europe is 743.1 million, we can estimate the total percentage of bike owners in Europe to be 35.5% (263.8 / 743.1). If, as in the Netherlands, 53% of those who own bikes use them recreationally, this suggests that overall participation in recreational biking is about 18.8% (35.5% x 53%) in Europe.
This is both very close to and slightly above the 17% reported in the 2005 study. Since as we will show below, cycling as a leisure activity has been on a slight rise in at least some areas of Europe, we have high confidence that 18.8% of Europeans consider themselves non-professional cyclists.
AMATEUR CYCLING BY COUNTRY
In 2013, 9.92 million Germans age 14 and up engaged in recreational cycling several times a week. (More recent information was not available in the public abstract.) Since Germany's population in 2013 was 80.65 million, and 88.95% are over age 14, this is equivalent to 13.8% of the population (9.92 / (80.65 x 88.95%)).
In Spain, 38.7% of the population claims to cycle recreationally, but only 10.3% participate on a weekly basis. However, this is up from 6.7% who biked weekly in 2010.
In France, in 2005, 13.3% of the population over age 15 participated in biking at least once a year. Despite a thorough search, we were unable to find a more recent statistic in any English-language source. Based on the rest of our study, we believe this to still be accurate within a couple of percentage points.
In 2005, about 9% of the UK's population participated in recreational cycling, a number that has risen to 13.9% today.
Based on the most recent available studies, we triangulate that 18.8% of Europeans consider themselves non-professional cyclists, up from 17% in 2005. This includes 13.8% of Germans over the age of 14, 10.3% of adults in Spain, as much as 13.3% of the French, and 13.9% of adults in the UK.