PSG's squad may not have any big-name star players. But the bonding between the players in PSG's squad is very strong. So if the players of PSG can continue this kind of performance then there is a possibility of this team performing well in the Champions League as well. Due to the good understanding between the players, the team played well in all three matches in Ligue 1 and managed to win each match by a big margin. PSG got an experienced coach like Luis Enrique. Luis Enrique is also an experienced coach for the Champions League platform. So I think PSG has a great chance to do well in Champions League matches this season.
Having big names isn't necessary all the time to get the team winning any game, because even with big name at some point, a team has lost still so it's mainly the tactical reference and strategy of a team that gets them to doing as better as they really can, only a few still make it really big with big names, some actually do fail and some times the big names in the team ends up not shining bright because of the environment typically but a better one for them helps them get the magic done for them.
PSG dominate Ligue 1 and are the biggest contenders for the title in their league every season. Mbappe's departure is not a problem for them. Because Luis Enrique didn't build his team on Mbappe and this allows them to play a stable game in the league. But I don't think PSG have enough squad to compete in the Champions League, you need big players and magicians and PSG lack the players who can save games. If you think of Real Madrid, Manchester City or even Barcelona, I would say that PSG will have a very difficult task in the Champions League with their current squad.