I found an explanation of yellow card in Peter Hays, The Critical Reception of Hemingway's The Sun Also Rises (2011):
But on the subject of Parisian whores, [the critic Michael] Reynolds makes an important correction. At the bal musette Georgette flashes her yellow card, her license as a prostitute, a license that necessitated regular examinations for venereal disease (SAR 36). When she tells Jake, "Everybody's sick. I'm sick, too" (SAR 23), it is not venereal disease to which she is referring, as many readers and critics have assumed. As Reynolds says, "it is not sickness of the flesh but of the spirit, and in that sense everybody in the novel is, indeed, sick" (76).
It is thus not a slang term. Instead, it refers to what is, literally, a yellow card issued by the government and affirming that the government's medical authorities have checked the bearer within the past year for venereal diseases and found that she did not (at that time) have any.