The bold, brash French giants talk a good game, and their Qatari owners have thrown vast sums over nearly a decade now in an attempt to build the best side in Europe.
Yet for the third year running they are out of Europe's elite club competition in the first knockout round after Wednesday's stunning defeat on away goals against Manchester United.
Coaches have come and gone, superstars have been signed, but in the Champions League all PSG seem able to achieve is to invent new and improbable ways to be eliminated.
In 2017, after the promise of four successive quarter-final appearances, there was the capitulation in Barcelona, a 6-1 defeat wiping out a 4-0 first-leg win.
Since then, Qatar Sports Investments have spent over 500 million euros ($565 million) in transfer fees on new signings, including the two most expensive players in the world, Neymar and Kylian Mbappe.
There has been no progress, and there must be some uncertainty as to the long-term viability of the Qatari project, especially with the danger of punishment still looming for possible breaches of UEFA's Financial Fair Play rules.
Last year, there was an underwhelming defeat against Real Madrid, with Neymar injured for the second leg. This time, with Neymar again injured and Mbappe off form, PSG were ousted by a seriously depleted United.
The visitors had two untried teenagers on as substitutes when Marcus Rashford scored the last-gasp penalty -- awarded after a controversial VAR review -- that gave them a 3-1 win on the night.
It feels like Goundhog day, but this time it is somehow different.
"Even worse" read the front page of leading sports daily L'Equipe on Thursday, with a nod to that night in Barcelona.
Inside, renowned commentator Vincent Duluc said PSG "owe much of their celebrity to these collapses that make them look ridiculous in the eyes of the world."
Against United, seven survivors from the Barcelona debacle either started or came off the bench. Was that game on their minds?
"I don't agree that we have a problem from losing at Barcelona that you could see," said coach Thomas Tuchel. "This is for me too easy and I don't want to step into this trap."
However, even their exit to Chelsea in the 2014 quarter-finals was similar in nature.
Abroad, PSG, founded in 1970, are often derided as having no history, seen as a club with vast amounts of money, but no substance. They are now the serial Champions League bottlers.
'Believe in this project'
So what comes next at the Parc des Princes?
Financially, PSG will still have made an estimated 85 million euros from their European run this season, and they recently announced a lucrative, new shirt sponsorship deal with Accor reportedly worth over 50 million euros annually.
President Nasser al-Khelaifi will come under scrutiny, and one of either sporting director Antero Henrique or coach Tuchel will probably have to go. It is more likely to be the former.
"We are here because we believe in this project and in the direction in which it is heading," insisted Brazilian defender Marquinhos.
He played in midfield against United, with French international Adrien Rabiot frozen out after refusing to sign a new deal.
With hindsight, Tuchel may wish he had started Alphonse Areola in goal rather than a 41-year-old Gianluigi Buffon, at fault for United's second goal.
Tuchel can still win a league and cup double, but winning a domestic treble was not good enough for Unai Emery last year.
"We must not say the season is finished," said Al-Khelaifi, although he admitted "it's difficult to come back from this."
As long as the current owners stay, they will try, but Neymar's future will again now be called into question.
The Brazilian's two years in Paris have been overshadowed by injuries at key moments. His chances of winning the Ballon d'Or are surely over for another year.
In the meantime, the hangover will be long and painful.
"I need some time to rest. I want to be at home and not talk, not think. I just can't believe that this is possible," admitted a shattered Tuchel.