This is a short, relaxed itinerary for 3 days in Paris. For this, try to arrive Paris in the morning. Check in at the hotel is at 2PM but you can leave your luggage at the front desk. The hotel recommended is in the central area of Paris. It is about 200 yards from Luxembourg RER Station so it is very convenient.
After dropping off your stuff, start Day 1. The Luxembourg Palace & Luxembourg Gardens are very close the hotel, so visit them first. There are many restaurants in the area so you can pick one for food. Continue your day by walking toward the Louvre via St. Germain. This is one of the most classically Parisian neighborhoods. Next will the Louvre. I highly suggest a guided tour. After this, go watch the sunset over the Eiffel Tower from the Trocadero Gardens. It is quite a long walk so I suggest for you to take the metro. I think this is the best way to end your first day in Paris.
On Day 2, visit the Arc de Triomphe as early as you can as it can get really busy. Go up the rooftop and tour around it. I highly recommend a skip the line ticket for your convenience. Walk towards the Champs-Elysses, the shopping district. Shop or simply look and take photos. Then, slip away from Paris for the afternoon to Versailles. The travel is about an hour to Versailles and it is not the main metro. You will to take the RER C line.
On your Day 3, Be sure to enjoy a Parisian Brunch: Appetizers, a main course, a cheese course (to follow the meat course, as is typical in France), a dessert, and–obviously–wine.
Remember that there are 2 airports in Paris: Paris – Orly Airport and Paris – Charles de Gaulle Airport.
Make sure you go the the correct one for your return flight. Allow ample time for travel, check in, and passport control. Take home your memories of this lovely city!