My knowledge of the time period is more Italian focused than French or Low Countries focused. Still, there you can really see the importance of urban leaders and their relations with both the nobility (who were often a sort of semi-urban nobility who had their power bases in the country-side but at least partially resided in and exerted power in the cities) and the lower classes. That said, there was no central government in some of the places I will mention, since these were city-states.

For Roman history, it might be interesting to look at the (admittedly extreme) example of Cola di Rienzi. The Life of Cola di Rienzi translated and edited, I believe, by John Wright (I don't have my copy with me). It's an account of Cola's use of the mob to establish good government in the city and how things go horribly wrong. It's light on really intimate details, but gives an enjoyable account of his relationship with the popes (and their vicars), the local nobility (namely the Colonna), and "the mob" (whom he relied on for his power). The book uses excerpts from a longer, more detailed chronicle of Roman history that (I believe) does not exist in English translation. For a good modern source on the topic, I would recommend Apocalypse in Rome by Ronald G Musto, though a number of books have been written on Cola's rule in Rome.

In Florence, a great primary source on the very topic you're interested in would be the Nuova Cronica by the Villani family, which is a chronicle of Florentine history. I believe that the most recent English translation is just over 100 years old, so not exactly up to date (but in the public domain!). Still, the chronicle is incredibly detailed and mainly covers the events of the 14th century (when the chronicle was written). For a more readable and entertaining history, Leonardo Bruni's History of the Florentine People is a great account of the city of Florence's political history. It primarily covers the period from 1260 to the early 15th century. It doesn't go into the minutiae of urban government, but it does give great details on the reforms of Giano della Bella and has an account of the Revolt of the Ciompi. Macchiavelli's History of Florence could also be read as a sort of counter-Bruni text on the same topic (though it covers more history in less detail). Guicciardini's History of Florence and larger History of Italy also cover some of these topics very well, though the latter is more focused on the wars that devastated Italy in the early 16th century.

For Venetian urban history, unfortunately the main Renaissance historian of the city, Sabellicus, was sort of lacklustre in his quality and his work is of such great size that it doesn't exist in translation. Bembo's History of Venice is mainly focused on the international affairs of the Italian Wars that overwhelmed the peninsula in the early 16th century, but also touches on internal affairs within the Republic. Bembo, like Guicciardini, wrote about times outside of your main focus, but it's still somewhat relevant.

If you want to go back in history, accounts of the Investiture Controversy as it manifested in Northern Italy, the origins of the Guelph-Ghibelline conflict, and the Lombard League could all be relevant to your interests. I've also mainly provided primary sources, since you mentioned having come to this interest via Froissart, but if you'd prefer more modern histories of the topic, let me know and I can look through my books.