What do you expect? When Chelsea was failing in the CL between 2003 until 2012, most of the football world was laughing too. In particular in the beginning when they were burning money left and right. Similarly with Man City.
You must be living in a fantasy world if you think that fans of elite clubs in Europe whose success is mostly down to their own hard work, sometimes for over 100 years, or fans of average clubs who can only dream about being bought by Qataris, Saudi Arabians or other people with endless money, would respect teams and clubs like PSG who are only where they are due to dirty Qatari gas money and a corrupt UEFA BENDING the rules for them. Much like for Man City as recently exposed and which was an open secret for anyone that has an IQ above 100.
As for the rivalry part, not true. We have played against each other in the CL knockout stage (round of 16 and quarterfinals) 3 times in 7 seasons. That is almost every second season. 2 of those ties were highly dramatic with one of them even containing the greatest CL comeback in history to date. No small feat.
That added to the Neymar transfer in 2017 (record transfer fee to date and a very controversial one), before that Thiago Silva, Marquinhos and Verratti transfer sagas, and there is a real genuine rivalry in the recent era much like our rivalry with another "nouveau riche" club in Chelsea back in the day. Not to mention the bad ties between our two boards and the whole Qatar Airways sponsorship that we ended.
So yes, there is a rivalry but a very one-sided rivalry that is in our favor sporting wise (completely) so far. Nevertheless a rivalry. If you ask the average PSG fan from Paris they will list us as our main rivals in Europe IF not the main rival. Pretending otherwise is quite foolish.
EDIT: Even forgot our recent interest in the GOAT Rabiot to make matters even worse.