This study provides a large-scale mapping of the French media space using digital methods to estimate political polarization and to study information circuits. We collect data about the production and circulation of online news stories in France over the course of one year, adopting a multi-layer perspective on the media ecosystem. We source our data from websites, Twitter and Facebook. We also identify a certain number of important structural features. A stochastic block model of the hyperlinks structure shows the systematic rejection of counter-informational press in a separate cluster which hardly receives any attention from the mainstream media. Counter-informational sub-spaces are also peripheral on the consumption side. We measure their respective audiences on Twitter and Facebook and do not observe a large discrepancy between both social networks, with counter-information space, far right and far left media gathering limited audiences. Finally, we also measure the ideological distribution of news stories using Twitter data, which also suggests that the French media landscape is quite balanced. We therefore conclude that the French media ecosystem does not suffer from the same level of polarization as the US media ecosystem. The comparison with the American situation also allows us to consolidate a result from studies on disinformation: the polarization of the journalistic space and the circulation of fake news are phenomena that only become more widespread when dominant and influential actors in the political or journalistic space spread topics and dubious content originally circulating in the fringe of the information space.