I don’t particularly think that without Mbappe, PSG will face hardships. At least not in Ligue 1. Football is not played by 1vs11, rather it's a team game. Yes, it can be argued that Barca became arguably worse after Messi's departure but they weren't really that good when he left.
If you talk about PSG, they have good finances, a solid coach, and a decent amount of players in the club still. If they play their cards right, they can still dominate the Ligue 1.
About the UCL, Luis Enrique would need good reinforcements, as they couldn’t win it even with Mbappe. He needs to sign a proper striker and then need to balance out the whole squad, and if they do that, they might do well in the knockouts.
Talking about Mbappe's absence, it will only affect the team's performance in the Champions League not in League One.
PSG will remain the best team in League One because I don't think there is any other team in the tournament that comes close to them in terms of performance since they have been dominating the League One for a long even when Mbappe and other star players are injured.
Since the team has money, they should give Luis Enrique some money to shop for more players that can help the team achieve their main aim which winning the Champions League; if they don't add some quality players, they will do well in the League one, but can fail when it comes to Champions League.