// written in the heart of the night so you are in for a messy and sometimes off-topic read !
It's stating the obvious but the influence of any western city of the world is much more weakened now compared to the previous centuries, because of demographic evolution,emerging economies and globalization. I don't think you will ever have again cities in the world that influence the rest of the world on their own, the world is too multi-polar now with cities developing in east-Asia, middle-east or central Africa. For example we don't hear much about NYC anymore in France nowadays while it was still praised when we were kids. Global interconnection is so that, be it in the social or the cultural field, a new trend in a country will be more easily quickly known, copied or adapted in the other countries. Well except when some dictatorial countries decide to isolate themselves...
After saying that, I disagree to qualify Paris as a big museum : in fact I tend to think Paris is quite dynamic, at least for the last 15 years, and this for better and worst. And the future of Paris lies in what will be the Grand Paris, in terms of urbanism, regional decentralization, culture, sociology (kudos to www.enlargeyourparis.fr to show what happens beyond the périphérique)