Paris is a very special place. If you have never been to France, go to Paris first, and then expand your travels. Paris is wonderful no matter what the weather is. When you stay in Paris, you do not need to make any plans. You can just leave your hotel, pick any direction and you will have a great time. You can pick almost any sidewalk cafe and get a good meal. Make sure you take a walk from the Louvre, through the Tuileries, and up the Champs Elysees to the Arc de Triumphe. I also recommend taking a boat ride on the Bateau Mouche down the Seine. Even though I mention Versailles below, it has it’s own page.
If you must make plans while in Paris, there is a long list of must see places. The Arc De Triumphe (above), the Champs Elysees, Rodin Museum, Invalides, Louvre Museum, Tour Eiffel, Tuileries, Latin Quarter, The Marais District, and Pont Neuf to name a few. You will need a minimum of 5 days to visit Paris the first time. The Louvre takes an entire day to see by itself. You can get away with 3 days after that. Most of the museums are open 9-6pm daily except Mondays. Most are closed on Monday. Check before you go.
Take another day to visit Chateau Versailles. Take the RER C from Paris to Rive Gauche in Versailles. It’s about 1/2 hour ride. The trains are named Vick and Cime. The Chateau is about 2 blocks from the train station.