The Paris Métro system is extensive and often more cost-effective than taxis or rideshares. Consider purchasing a Paris Visite pass for unlimited travel on buses, trams, and the Métro for a set number of days.
While areas like the Marais or Saint-Germain are popular and centrally located, you can save on accommodation by staying in less touristy areas like Belleville or the 13th arrondissement and still easily access main attractions via public transport.
Avoid restaurants in tourist-heavy areas. Instead, opt for local bistros or purchase fresh produce from local markets and have a picnic in one of Paris's many parks. Also, look for restaurants that offer a "formule" or a set menu for lunch — they're usually more affordable.