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.
The french ligue 1 has two tittle contenders PSG and others. PSG has dominated the french league in the last 10 years and they have won it 8 out of 10. But when it comes to Europe they are no where to be found, their most desired trophy, the champions league trophy is always out of their grasp yearly no matter how much the spend in the transfer market.
They have sought the services of different mangers to make this dream a reality but none have been able to deliver their most desired trophy. I think they will have a great shot at winning the champions league if they can clinch the services Zidane. He's well experienced and his records in the tournament is remarkable.