I wear black jeans that read as slacks and a turtleneck in winter and at most throw on a fancy shawl or top over that if going to a nice place for dinner or the opera. There are few places that dressing up is necessary.
The problem in museums is what to do with your coat. IN the Louvre, it is easy; there are lockers and so no long lines to check coats. The Musee d'Orsay is the worst. I have waited in line to check coats for 40 minutes. So now I always carry a nylon carry bag -- the kind that folds up and can go in a pocket, but it pretty large and stuff my coat into that while in the galleries. I will never line up for coat check at the Orsay again. The Jeu de Paum has lockers as well. We didn't look for coat storage at the Pompidou but just carried our coats so not sure there.
People at the Philharmonie are not dressed up in our experience. It is a wonderful building; get there early so you can go up to the roof and get a good look at the building. They do have coat check.
I'd wear clothing while you are out and about that is sort of dressy casual e.g. dark pants and a sweater or nice shirt andn ot worry about 'dress codes'. Pretty much everyone is in jeans and trainers in Paris -- ideally you get dark athletic shoes but you see plenty of light colored ones as well. The only place I have been with an explicit dress code was Tour d'Argent and that was 8 or 9 years ago. I just threw a pretty shawl over my basic black and wore black casual shoes rather than my lightweight hiking boots for that event.