I think the reason why PSG can't compete fiercely in the Champion League competition is because League 1 is not competitive even in the last few seasons no team has put pressure on PSG to defend its title and it's all because of PSG's financial strength which is above average of other teams.
And I'm even sure that for the next few seasons it will be difficult for other teams to compete with PSG unless the team management is willing to spend more money to buy quality players in all lines.
In last one decade usually PSG management were doing decisions which were never been positive and suitable now first time they are having few good things which are going to help them in long run firstly team is looking much better and competitive without big names.
Secondly now they are also having good faith into coach and giving him extension which is good while in this season early games were no good in Champions League, but now they are having spot into round of 16 which is big success coming season could be much better and positive because players will be having experience and good depth. Now facing Liverpool is big challenge but still good because after beating Manchester City their confidence level is improved, and they are feeling good which will help them for having good performance against Liverpool and keep their hopes alive for next round as well.