What PSG gets this season will really determine the fate of Kylian Mbappe, but unfortunately he will not think about the Ligue 1 title because he has already had it for several seasons, not only when he was at PSG but when he was still at Monaco he already got it.
The Champions League title is the target and it is the same as the target of the club owner, and the question is whether PSG will be able to get it this season? It's hard to predict because PSG will have difficulties when they enter the knockout phase because in the Champions League there are teams that are more solid than them in terms of appearance. We will see developments regarding the status of his contract at PSG, if he extends it then he will stay here but if there is no extension then he will move and Real Madrid will be the main destination, but many things could happen because he could change his mind.
Considering they have won ligue 1 and still fired many managers before thinking that is not enough at all (they are right) then I am guessing that the fate of Mbappe will not be decided based on what they will win this season neither. If they win the league, they will not care about that, it's normal for them to win, hell that Lille win season was the worst thing that could have happened for them. They have to win it already, if they lose it somehow then it is going to be one of the worst without a doubt, and they should rethink what they are doing.
I think it is quite obvious that we are going to end up with something that would be a lot more important to change and should not be really changing anything that would ruin anyone's chances. The best thing to do in that case would be the fact that Mbappe could leave and the team would not have that much different result.