Actually, Arsenal has the ability to win the Champions League title, it's just that the competition is very difficult, especially since Arsenal has to face Real Madrid, Man City, Bayern Munich, Inter Milan, etc.
Meanwhile, Arsenal failed to win the Premier League title for 2 seasons and they were also eliminated in the Champions League before reaching the final.
Arsenal are strong and competitive but not enough to win Champions League. If they failed to win Premier League, it would be harder for them to win Champions League. It is still possible but if they win Premier League title first, their players will have more confidence, stronger mentality to fight in Champions League. It is not mandatory to win Premier League as a prerequisite to win Champions League but winning Champions League when don't have experience as champion in Premier League, is very small.
Which PSG coach are you referring to?
Mauricio Pochettino, Thomas Tuchel, Unai Emery, Laurent Blanc, and Carlo Ancelotti are few former coaches of PSG. None of them are bad coaches, even Ancelotti is the most successful coach in football history, especially in UCL. I think PSG is just unlucky that they always failed to win UCL.
https://www.worldfootball.net/teams/paris-saint-germain/9/Well, Luis Enrique is the coach of PSG now. He is also a great coach, but not sure if he is able to lead PSG winning UCL trophy. FYI, he also ever won UCL trophy with Barcelona.
They are great coach but only Ancelotti had experience of winning Champions League before joining PSG. None of Pochettino, Tuchel, Emery, Blanc won Champions League, except Tuchet with 1 Champions League title after leaving PSG to join Chelsea.
This detail is not to prove these coaches are not good enough and failure of PSG comes from their board members that gave too many power to star players. Players also failed to show their values to help PSG winning Champions League. Many imperfection in PSG system and problems are not only from their coaches.