score:12
Fortunately, Wikipedians maintain a list of French royal mistresses, so we can knock off a whole slew of Kings at once (link). The list starts with Clovis I and ends with Napoleon III: the A-Z of French royal infidelity.
Any king not on that list is a candidate for having been a faithful husband. I'll suggest that Saint Louis IX was among the most likely to have been faithful. Discussions of his sex life suggest that although he loved his wife and had eleven children with her, he was still pretty good with self-control:
If one were to pass judgment on the marital life of Louis IX, one could say without reservation that it fulfilled all the requirements made by Pope Piux XI in his encyclical on marriage, Casti connubii. It was a chaste marriage, in which there was no misuse of the marriage right . . . Ever since their youth they had faithfully practiced marital continence . . . The biographers explicitly report that they observed continence during the so-called "days of abstinence" in the liturgical year, in Advent and Lent, also on Friday and Saturday of each week, and, furthermore, for one day before and one day after the reception of Holy Communion . . . It goes without saying that sexual abstinence was also practiced in the marriage whenever the wife was pregnant . . .
After lots of Googling and Google book-searching, I haven't found any mention of courtesans, affairs, or mistresses associated with Louis IX. Given the amount of historiographical interest in Louis IX, and given that biographers were apparently familiar with his sex life, Louis IX seems as "probably chaste" as any of the other French kings left off that list.
Upvote:1
King Louis VII was probably one such king. His first wife, Eleanor of Acquitaine (in)famously complained that he was "more of a monk than a man." When they got married (as teenagers), he donated her wedding gift, a valuable rock crystal vase, to the St. Denis Basilica (church).