PSG is not after Ligue 1 because the chances that it will win it is very high, but it has not won champions league, that is what PSG is after now, they need to win champions league. With the present squad it is having now, the players are very talented and PSG is now stronger than before, though we have not seen the outcome result but they will prove us right very soon. The competition for champions league is high but the chance that PSG will win it is very higher than before.
Having basically every good free transfer in one off-season will get you to that level. I am not saying that they will win UCL this season, we never know who will win, sometimes even the best teams end up losing, look at Liverpool a year before, they won the league with very few losses, didn't lose for like 30 games or something, went unbeaten in the league, but at UCL they sucked so bad, it is not always the same thing.
PSG could dominate ligue 1 very easily, but that doesn't mean that they will be winning UCL, that is a whole another beast that requires a lot more attention and sometimes even one bad game sees you out and that is how great teams end up losing. I believe that PSG has a big challenge ahead of them, but this is their first year together with this core group, they are not even all there yet, Messi will be ready like in September, so it is going to take a while, maybe next season they can be even better? That seems like a better chance for them.