In short
Paris is lived by arrondissement rather than by monument. The working-class north-east, the bourgeois west, the university Left Bank: three different cities, fifteen minutes apart on the métro.
Everything is reachable on foot or by métro, which stays rare for a capital this size.
What it really costs
Housing crushes the budget: it often takes more than half the month, and studios under twenty square metres are the norm downtown.
Culture, by contrast, is cheap: museums are free on certain days, and an unlimited transit pass costs less than a parking space.
What nobody tells you
Tourist saturation downtown is real. Montmartre and the Marais are unlivable in summer.
Finding a flat means a full application file and a French guarantor. Without French income most agencies refuse, and you end up in sublets or furnished residences.