We do have some secular poetry; in fact a great deal of medieval literature was written in verse, including the Old English epic Beowulf.
Scholars are fairly sure, based on a few fragments and on references in historic texts, that much lost secular poetry was set to music, and was spread by traveling minstrels, or bards, across Europe.
One of the features of the Renaissance which marked the end of the medieval period is the rise in the use of the vernacular or the language of the common people for literature.
The compositions in these local languages were often about the legends and history of the areas in which they were written which gave the people some form of national identity.
The formality which Latin had gained through its long written history was often not present in the vernaculars which began producing poetry, and so new techniques and structures emerged, often derived from oral literature.