That's where you live.
Where "I" live (France), a company can't go, and flirt with a dude in another company of the same sector. Trying to steal employees is forbidden. Sure still many does it, but if you get caught, oh boy.
Also, I can't resign just like that to join a competitor. Each contract has some clauses, for example in mine, I can't resign to join a company from the same sector (well I can still go to court, or ask for a mediation, but still, 2 months of mercato would not be enought to pull it out

). Also all companies have the right to ask you to stay for [see clauses in your contract to see how long] so that they can find replacements, or to give time to your company to form a new employee.
Which is logical, imagine if you get employed just to steal documents, and secrets. You stay one month to get what you want, you resign, and join the first competitor around. Nope, doesn't work like that here. Not easy at all to pull it off.
If you compare with football clubs that are big companies, it isn't as easy to leave a big company (like where I work) to join a competitor. So yeah, i'm not shocked at PSG claiming they are in the right here.
Hard to compare between countries. I can do it with Verratti tho, because the dude "works" in the same country as me. And here a company that treats you well have some rights too.
edit: Just like about firing somebody if you're the boss, in France, you can't fire anyone without any reason (yep you need a reason, a real one, not just some bad excuse), or get your ass ready to be sued.