The French situation is a bit comical.
Theoretically the French state has a monopoly over all money games, so that would make online poker playing illegal. But that monopoly itself is illegal according to European laws that supersede the French law in this case.
Practically, players are free to do as they like, but site operators cannot operate from the French territory. Which is fine since they are all in Malta, Gibraltar or the Isle of Man anyway.
The main concern of the French government is actually horse betting and lotteries, not poker. Indeed, horse betting is the major income source for the whole horse racing economy and losing the PMU's monopoly on it would jeopardize it. And lotteries is a major tax resource.
All this is of course presented by the government as a noble fight against problem gambling, which is pretty ridiculous considering the monopolistic lottery offers some of the most addictive games ever invented and even has automatic lottery ticket dispensers in public spaces which of course make age verification a little problematic.