PSG‘s claim to fame for the 30 years prior to Qatar was having Ronaldinho play for them. I think they had 1 league title in their entire history.
2 league titles, 9 podium appearances besides, 1 win in C2 (and appearing in the final the year after, semi the year before), 1 CL semi in 94/95. Arguably the second most successful French club on the European level behind OM and its CL win (+ C3 final). Though France always underperformed historically there.
Second most popular club in France still before QSI's arrival (behind OM again), Lyon being the only team entering that conversation in the 2000s.
In a sporting sense thatyve definitely failed. The only worthwhile achievement they could have a achieved is the Champions League and they've failed at that and at this stage their team seems to be going backwards in terms of quality with ffp and the owners not likely willing to splash in the same manner as they did when they arrived. France was such a weird league for Qatar to have chosen for this project considering the French league has never been lucrative and their arrival has certainly not made things much better for the rest of the league, they could have bought a club in the PL or LA liga and done so much better commercially.
I think the choice of France was driven by larger considerations, Gulf monarchies were less common as public facing actors as they seem to have been in the UK (for colonial and post-colonial reasons). Talk among PSG fans back during the transition from Colony to QSI speculated a lot about the real estate in and around the stadium. The Parc des Princes is sitting in one of the wealthiest districts of the city (much to the annoyance of locals), nearby Roland-Garros.
Paris is also obviously a lot more lucrative, glamourous, visible, marketable and central (besides sitting at the heart of one of Europe's most important countries) than most cities. More importantly it could be captured, football-wise & unlike London, just through PSG.
I think Paris, besides specifically targeting France on a charm offensive for massive increased economic exchanges, offered the most returns with the most guarantees. The French top league sits in a weird space where it should be part of a top 5 by virtue of the funds and size but -as been noted- is competing performance wise with Portugal and the Netherlands at the club level (and European legacy, where you could add Belgium as a contender).
Yes, in hindsight, being a whale in a pond may be holding them back. The price to compete with them long term in Ligue 1 would be now so prohibitive it's doubtful it will happen. Marseille and Monaco are the two places that could be attractive to billionaires but OM has its own shares of systemic issues.
I do think however there were sensible, genuine arguments to choose the path of least resistance over the Premier League. Avoiding direct competition with other Gulf states which may have been too overtly political and interfered with the sportwashing aspect. Too crowded with competition in general and rife with potential failure... QSI was not entering the game to be another Fulham, Everton or Leicester. I think being a perennial Champion's League contender is more valuable to QSI than struggling for or below the British top 6.
It also boiled down to timing and opportunity : Colony Capital bought PSG in 2008 ostensibly to flip it at a profit. Not sure there was a comparable, suitable PL club available in that period.