No. But they could ban American companies from providing services directly to that French publisher (e.g., a US company couldn't print books for or sell paper to that French publisher). However, a US law could not stop me from legally reading a copy I owned, or from selling or giving that copy to someone else within the US...
The First Amendment case would be much clearer if this was actually about banning access to TikTok (it's not: TikTok self-blocked US users, Amazon/Oracle shut off servers, and app stores stopped distributing to US users). TikTok could choose to operate their service (like many other Chinese companies) using only non-US infra and without relying on American companies to distribute their app; indeed, the Chinese version of TikTok, Douyin, hosted entirely from Chinese servers, continued to work just fine.
This case is also a reminder of why the iOS App Store is so bad for rights: at least on Android, you could sideload a 'banned' app; Google can comply with the law and US users can still download TikTok. On iOS, you don't have that option.
The First Amendment case would be much clearer if this was actually about banning access to TikTok (it's not: TikTok self-blocked US users, Amazon/Oracle shut off servers, and app stores stopped distributing to US users). TikTok could choose to operate their service (like many other Chinese companies) using only non-US infra and without relying on American companies to distribute their app; indeed, the Chinese version of TikTok, Douyin, hosted entirely from Chinese servers, continued to work just fine.
This case is also a reminder of why the iOS App Store is so bad for rights: at least on Android, you could sideload a 'banned' app; Google can comply with the law and US users can still download TikTok. On iOS, you don't have that option.