Tractate Sofrim (14:14) records two opinions that concern the wearing of a head covering during the Shema: there are those who say that it is not necessary, and there are those who say that it is necessary, since one whose head is uncovered may not pronounce the name of God. According to the Bet Yosef (Tur, OC 91:3), the halakha is in accordance with the latter opinion (that a head covering must be worn), since that was the opinion codified by Rabbeinu Yerucham (Sefer Toldot 16:7, 148d).
Interestingly, the Darkhei Moshe (Tur, OC 282:1) records the fact that there was a French custom to follow the other opinion, and not to wear a head covering when reading Torah. His source for this is the Or Zarua, which notes ([II:43]) that this was not merely a local custom, but something that the Rabbonim in France were doing.
The gradual stabilisation of the custom of wearing a head covering all day long was at times a controversial subject (with yarmulkes occasionally being drawn onto the heads of rabbis in drawings), but the image of bareheaded men reading Torah or reciting Shema is striking.
To which rabbonim in France was the Or Zarua referring? Did Rashi wear a yarmulke? Did he ever discuss the obligation to do so in his responsa?