Participatory democracy and public consultations are increasingly being used to shape public policy or resolve political issues. In France, the Grand Débat was launched in early 2019 as a democratic response to the Yellow Vests movement, a massive grassroots social protest. With more than 500,000 participants, the Grand Débat platform was interpreted as a popular success by the government and the media, but little is known about which citizens expressed their opinions online. Although participants on the platform were anonymous and only answered public policy questions, we are able to infer their support for the Yellow Vests movement by using a second platform (a Facebook app) that asks similar questions as well as support for the Yellow Vests. We find that a large majority of participants in the Grand Débat did not support the Yellow Vests movement, in contrast to the general population at the time. This is evidence of a strong self-selection of participants on political grounds, resulting in a biased representation of French public opinion.