I assume PSG wouldn't have much problem on securing their Ligue 1 championship from now on. However their main goal was to win the Champions League title but they were pushed out of the tournament very early. In this case Galtier would be blamed for this result most probably. The Ligue 1 is already easy for them but they still don't have any title in the Champions League.
I expect PSG to be in search of a much better manager than Galtier in the summer. I don't think he would stay longer.
It is clear that in Ligue 1 they will be able to become champions without significant pressure, but the problem is that their main goal is not in Ligue 1 but in the Champions League. And as you said they were knocked out by Bayern Munich in the round of 16. Of course this will be a threat to their coaching position which means perhaps their failure in the Champions League will result in their coach being sacked early.