The number of days needed to explore Paris can vary depending on your interests and pace, but a good rule of thumb is to spend at least 4-5 days in Paris.
Here's a suggested Itinerary:
Day 1: Explore the Eiffel Tower and its surroundings, including Trocadéro and the Champ de Mars. You can also visit the nearby Musée du Quai Branly, which showcases indigenous art and cultures from Africa, Asia, Oceania, and the Americas.
Day 2: Visit the Louvre Museum in the morning, and then stroll through the Tuileries Garden to the Place de la Concorde. From there, you can walk up the Champs-Élysées to the Arc de Triomphe.
Day 3: Dedicate this day to exploring the islands in the Seine: Île de la Cité and Île Saint-Louis. This is where you'll find Notre-Dame Cathedral and Sainte-Chapelle. Nearby, on the right bank of the Seine, you can also visit the Pompidou Centre, which houses the National Museum of Modern Art.
Day 4: Visit the Musée d'Orsay in the morning, and then head over to the Latin Quarter to see the Panthéon and wander around the Sorbonne University area. End the day at the Luxembourg Gardens, a perfect spot to relax.
Day 5: Take a day trip to the Palace of Versailles. Spend the day exploring the palace and its magnificent gardens.
Of course, this doesn't take into account additional attractions like Montmartre, the Opera Garnier, the many charming neighborhoods (Marais, Belleville, Montparnasse, etc.), or other great museums like the Rodin Museum or the Picasso Museum.
So if you want a more relaxed pace or if you want to explore more of what the city has to offer, you might want to consider staying a week or even two. And even then, you're likely to leave with reasons to come back! Paris is a city that always has more to offer.