You'd expect it to be the other way around.
Perhaps Twitter should start demanding payments from French news organizations to offset these royalties and ban links to those who refuse.
Twitter is using a headline and maybe an image, provided by the news organizations specifically to act as an advertisement to get people to click on it and a link.
In this case, the value being provided to the news organizations is almost certainly higher than the value provided to Twitter. Meta certainly seems to have thought so.
Certainly news organizations should be paid by those who find their products valuable, but demanding payment for small quotes, something supposedly protected by international treaties as fair use, seems rather hypocritical for news organizations who are in the business of quoting others.