First of all, I would contest that the Renaissance is a distinct time period buuuuuuut, there were many populist movements during the Middle Ages.

One could describe many of the heretical movements as populist/anti-establishment as many contested the sacraments, which were at the heart of everyday religious practice and helped to institutionalize the Church in the daily life of many inhabitants of Latin Christendom.

In terms of more explicitly political movements, however, in Italy, you have the Ciompi revolt, which was instigated by the wool carders guild that also represented all low-skill jobs and generally didn't have much power. They rose up and created a fairly radical government.

Cola di Rienzo was a Roman and the son of a tanner who declared the reestablishment of the Roman Republic with him as Tribune of the Plebs and sought to represent the populace of Rome against the machinations of the noble families that dominated the city.

Later medieval Italy is full of "populist" revolts.

The Boccanegra Revolt in 1339 Genoa. The popolo government of Bologna in the 1280s and that of Teddeo Pepoli in the beginning of the 14th century.

There were also a bunch in the Low Countries with which I am less familiar. Pieter de Coninck who led the pro-independence forces in the Franco-Flemish war could be called a populist leader.

You also have the Wat Tyler who rose up in England, accusing the advisers of King Richard II of misadvising their king and turning him away from caring for his people.

Edit: Cohn's Lust for Liberty is one of my favorite works of history and it deals with this topic.