This reading list in the FAQ is short of books on France in this period, so I'll recommend "A history of Sixteenth Century France, 1483-1598" by Janine Garrison. (Published in 1991, translated to English by Richard Rex, published in English in 1995). It's what I used once upon a time for my A-Level in history; it's very readable and well regarded.

It's much more concerned with the domestic side of France during this period, as well as the various foreign wars of Charles VIII, Louis XI, Francis I and Henri II. If you are exclusively interested with the papacy and the French Monarchy then it does have some detail of interest. However, this period (as you undoubtedly know) is dominated by the domestic wars of religion, which saw papal involvement increasingly against the king. (Culminating in the Guise, the Holy League and the papally sanctioned assassination of Henri III.)

To go on a tangent, Garrison argues that the St Bartholomew's day massacre was a primarily domestic concern. The widespread killing was not premeditated, and the "spark" (the killing of Protestant Nobleman under the auspices of the King) was "the reflex reaction of a regime with its back to the wall, caught between the rival pressures of the Huguenot leaders and the Spanish ambassadors, facing the risk of civil war on the one hand and war with Spain on the other"- not an appeasement or collaboration with the papacy (although it certainly was a collaboration with the hard line Catholic factions in France).

To sum up, if you can find more in depth books that look specifically at the period and subject that you're after then you might not need Garrison's book. But if you want a handle on the Wars of Religion in this time period (that are essential to understanding the role of the Catholic Church in France), then Garrison's book is excellent.

Good luck with your search!