I don't see Galtier being fired from PSG so soon, at least this season he won't be fired, even if I and many other people don't see him bringing good results, but PSG management still believes in the work he is doing in the PSG or else they don't fire him because maybe PSG's management doesn't want to spend a lot of money on contract termination, in my opinion PSG should go after zidane or the former coach of bayern galtier would be better options now for PSG, or they could also hire antonio conte who I believe would bring good results for PSG.
After eliminated from UEFA Champion League have many rumors about Christophe Galtier as PSG manager position will sack or not, but until today the rumor about sacked Galtier have gone and seems PSG management keep trust for him keep become PSG manager maybe next season.
Seems not have chance for signing Zidane because he has rejected many team offering from Manchester United and he still waiting become France head coach but need waiting for longer time. Actually, Antonio Conte is the best option for PSG but can't guarantee will be success in Champion League after failure with Tottenham Hotspur and eliminating on 16th round from AC Milan.