Fashionable informality is the rule for clothes in Paris. You can wear whatever you want, but you will feel much more at home if you dress carefully, whatever the style.
Have at least one dress-up outfit for nightlife (theater, ballet, orchestra, nightclub) and for that splurge in a more expensive restaurant.
Most of the time, though, tidy casual clothing is what's wanted. That's what most Parisians at leisure will be wearing.
In summer the city can be hot and humid, so you'll want light cottons for summer days, but a sweater or jacket at night.
In spring and autumn, have a sweater and jacket or topcoat, and an umbrella. Scarves are currently in in Paris, especially during these seasons.
In winter the weather can be quite cold and chilly, without much sunshine, so you'll want woolens.