There are likely bigger overarching trends at play, IMO. But Google as the biggest fish (and by extension other giants in the digital field) knows not only from the French action, but also the attempted Australian move and the October / 2020 lawsuit by the US Department of Justice re. its alleged antitrust behaviour in 'Search' that we're entering the Standard Oil / Sherman act break-up zone. Any nibbling away by individual countries or trade blocks at its near-monopoly power is viewed as part of this trend.
Google's 'Search' pages, at least in my country, not only include 'News' options but with it the news intro summaries and excerpts produced and paid for by publishing houses. My background is economics and computing, not law, and I don't know too much about the legal specifics of the Australian case, but Google clearly seems to employ its monopoly powers in 'News' as well. In essence, it has become the kiosk to browse the headlines of various offerings, such as those 'analog world' kiosks found in Paris, NY, London etc. with the newspapers and magazines aligned to show headlines and summary text the publishers arranged and paid for.
Finally, Google's threat response itself re. suspension of Search in Australia if the News segment is touched makes that connection...with Standard Oil it was also about horizontal and vertical integration.