A Yale history lecture has some figures which, though focused on England, might be applicable. The video of lecture 7, Late Medieval Religion and Its Critics discusses the number of clergy in England. Here's my transcription of the relevant section:
The clergy, who staffed this institution were a distinct estate of the
realm, as you already know. Attempts have been made to estimate their
numbers, its been estimated about 60,000 in all. Which would mean that
the clergy comprised about 4% of the entire national population.
@MCW posted a link to a Jstor article from 1944, THE CLERICAL POPULATION OF MEDIEVAL ENGLAND
by Josiah Cox Russell which is loaded with highly relevant information. (it also shows that any two sources of demographic information will inevitably differ). A snippet from that paper states:
The percentage of the clergy in the population should have been at
about its highest in the poll tax period, if these indications are
correct. If the total population was about 2,200,000 in 1377, the
combined numbers of the religious (10,600) and seculars (24,900)
should have been about 35,500 or 1.6 percent of the total population.
Omitting the nuns, the total is about 33,500 men or about three
percent of the male population.
So anywhere from 1.6% to 4% of the population according to these two sources, likely peaking in the period just after the Black Death in England.
As to why this time might have been the peak of the clergy as a percentage of the population, some relevant information might be gleaned from the Wikipedia article on the consequences of the Black Death in England.
Things of particular note here would be changes in the political structure with higher wages being available due to the shortage of labor;
By around 1400 serfdom was virtually extinct in England
the expansion of colleges such as Cambridge as an educational alternative to the monasteries; and the general disillusionment of the population with the church at the time (same wiki source-emphasis mine)
The clergy were seen to have an elevated status among ordinary people
and this was partly due to their purported closeness with God, being
his envoys on earth. However, as the church itself had given the cause
of the Black Death to be the impropriety of the behaviour of men, the
higher death rate among the clergy led the people to lose faith in the
Church as an institution
So this time period (abt. 1377 according to Russell) would represent the peak of the clergy's composition as a percentage of the population. From this time forward more opportunities were available to individuals that might otherwise have chosen a more pious lifestyle; hence the numbers of individuals entering the clergy was greatly outpaced by the population increase after the plagues. So more of this greater population, because of the social changes mentioned above, did other things.