Shortly after François I was crowned king of France, a procession was held commemorating the new king, said to be a celebration of le vit de François I. This title is a pun on the near homophony of the sixteenth century French words vie "life" and vit "penis"; the artists responsible drew a cart through the streets of Paris on which they displayed a gigantic sculpted penis and invited the populace to come flagellate it.
The motivation for the demonstration is unclear, but it arose in a cultural context which had been filled with phallic art in all media for the past several centuries.
In addition to the pilgrim badges discussed here previously, winged genitals regularly appear in manuscript marginalia; in some cases the penis-bird is depicted watching a couple copulate. Other motifs in marginalia include penis trees, sometimes depicted with people actively harvesting their fruit, as well as penises with bells tied around their shafts (more often seen in pilgrim badges). These representations are also attested in other media; there are, for example, multiple wooden caskets with carved ornamentation that includes the winged phallus motif prominently, and at least one with a penis tree.
Pilgrim badges and marginalia are also known for sometimes depicting anthropomorphic genitals carrying out some of the tasks of everyday life - including, in some cases, of religious life; there are pilgrim badges (!) depicting a mockery of Marian processions in which a vulva crowned with small penises is born aloft on a sedan carried by other, larger penises. (I've seen modern reproductions of this badge for sale, as well, because some jokes never get old.)
Other penises have been found which were carved from stone or cast in wax (the latter apparently for use in prayers for healing at a Christian pilgrimage site, at least if Thomas More is to be believed), and there is some evidence for the continuation into the late Middle Ages of the Roman custom of making loaves of bread in the shape of both male and female genitals. Small carved figurines with disproportionate members are also abundant. Vessels for wine, both for drinking out of and larger jugs for transporting it, are known with unambiguous phallic shapes, in both ceramic and glass.
Little is written about the precise meaning of the increase in phallic art during the late medieval and early modern periods. More's account of the (to his mind heretical) casting of wax penises as part of rituals for the treatment of kidney stones hints at one possible explanation; accounts of a phallic statue at one French pilgrimage site seem to reinforce this. It's also been postulated that the notion of provoking laughter as a means of warding off the evil eye may have something to do with it. Hypotheses involving fertility rites don't seem to fit; very few such ceremonies survived the arrival of Christianity in any form that makes explicit reference to the penis (though a few exceptions are known). It may simply be a fad for certain kinds of expression of the inherent human tendency to find our sex organs funny, with no deeper significance at all; if so, the artists of yesteryear did a great job, because people picking penis-fruit right off the tree is a joke that will grow stale only when there is no longer such a thing as a tree. And the bold procession for the Life of François I is a piece of comedic performance art which rivals the best of Improv Everywhere in its daring.