I don't know what exactly France did and why it does or doesn't work for them, but the article was less about the net number of new cases, and more about the impact of shutting down schools/society.
We know that, if you're vaccinated, you're both less likely to get COVID (not necessarily unlikely, with the new super-infectious variants, but less likely), and once you have it, are less likely to have a high viral load and thus spread it, especially if you don't have symptoms. If we knew that, for example, all of the diners and all of the staff at a restaurant were fully vaccinated, then the likelihood of catching COVID at that restaurant would be drastically reduced -- we'd still be exposed to the odd symptomless-but-contagious person as well as to the occasional person who has symptoms but decided to dine out anyhow, but it'd be very different math than "anyone working or dining here may not be vaccinated in the first place and may have attended an unvaxxed 300-person indoor wedding two days ago".
Same with schools: today, you can be an anti-vaxxer and send your kids to the same school as mine. Being an anti-vaxxer not only means that you're not vaccinated, but also that you're more likely to discount the entire pandemic and spend time in large gatherings with other unvaccinated people. And of course your children go with you. And you pick them up from school, and go to their basketball practice, and attend meetings.
By allowing willfully-unvaccinated people to seamlessly mingle with the rest of society, we're increasing everyone's risk. No one claims that by doing this we'll bring the number of cases down to zero, that's not actually the point. The point is that we'll be far less likely to catch COVID at any regulated place.