I am reading League of Dragons, by Naomi Novik, as an e-book. Based on the cover art I have the first edition. In Chapter 15, there is what looks like an "o" with a hat:
Laurence sighed privately. He would have been glad for a different ground-crew master, if he had dared ask for a replacement: O'Dea was clever enough, but untrained, and given to excess of both drink and poetic lamentations. In his case, Laurence would have had no compunction in removing him from the rôle and keeping him on as a personal secretary instead. But the Admiralty would surely...
Looking up the character on Wiktionary reveals that the hat is a circumflex and that this is an "Obsolete spelling of O". However, I'm not sure that this applies, since the examples given are for "ô" as a word by itself, while in the book it is just a letter in a larger word. Additionally, the narration restrains itself from too much period-speak, reserving that for in-world letters and the like. I got my hands on another e-book which allows searching; it seems that all instances of "rôle" have the hat.
Why does the "ô" in this "rôle" have a little hat?