I have been to Europe before and it's an overnight flight from the US to Paris so when we land we will be fine to explore that day.
You could be the exception, but for the majority of people flying overnight from North America, your arrival day will probably be at least a bit of a struggle to stay awake until after dark. Realistically, even before they get on a plane, many people start a trip with at least a bit of a sleep-deficit (maybe a large one), due to the inevitable pile-up of last minute work and pre-trip tasks. Sleeping on flights these days is a real challenge for many (its much better in business class, but if you're crammed in coach, and especially if you have a connecting city or two which makes for shorter individual flights but a longer itinerary), add in pre-trip stress that tends to build up, excitement for the trip ahead, and it's just not a great environment for getting rest. Some people (few, IME) can get good sleep under these conditions, but be realistic. Everyone can tough-it-out for a few hours, but most will start to fade soon. Most people set a goal of simply staying awake until after an (early) dinner on their arrival day, and I think that's an appropriate goal. Stay outside in the sunshine and fresh air, and keep moving. Avoid time indoors, in quiet places (eg museums). Maybe you will enjoy wandering Paris for several hours, but keep your expectations low for what you can accomplish that day.
Previous advice stands. You have five days there, not a week. If you keep telling yourself you have "a week" you will likely try to do too much/go too far. With five days, I'd stick to Paris and a day trip or two. But it's your trip. Good luck.