Paris is expensive but manageable with strategy. Budget travelers spending €80-110/day can stay in a hostel or budget hotel, buy baguettes and cheese from a supermarket for lunch, and take the Metro everywhere (Navigo weekly pass is excellent value). Many world-class museums — Musée d'Orsay, Louvre, Pompidou — are free the first Sunday of every month and for under-26s from EU countries.
Mid-range travelers (€150-220/day) can stay in a comfortable hotel, eat at proper bistros, and enjoy the full Paris experience. Eating a restaurant lunch (plat du jour) instead of dinner cuts food costs by 30-40% for the same quality.