Request a copy of the book The Louvre: All the Paintings through your local library. This book was published just last year, and contains color reproductions of all the paintings in the Louvre's permanent collection.
Quickly leaf through this book noting the five or six paintings you instinctively found the most beautiful and/or interesting, whether or not they're famous. If you need to pare down this list start by removing those paintings which are physically smallest, since the experience of looking at them in an art book will be closer to that of seeing the original.
Leaf through this book a second time looking only for art (generally reproduced in a larger size on the left-hand page) which had an impact on society beyond its impact on the art world. Try to narrow this second list down to five or six, but at a minimum it should probably include David's Oath of the Horatii and possibly The Coronation of Napoleon as well. Then, educate yourself to a basic degree about the role each played in world history (e.g. in the case of Oath of the Horatii at least read the Wikipedia pages for the painting itself as well as the page for the French Revolution).
When you actually arrive at the Louvre, spend up to a half-hour in front of each of the paintings you identified in steps 2 and 3 above, as if you were trying to memorize them, or as if you were alive at the time each was first shown.
Pick no more than two of the departments which exhibit three-dimensional art, and stroll through them at a medium pace. I'd recommend choosing the Roman art collection, then either the Islamic art collection or the sculpture collection depending on your interests.
Leave. In my opinion you can almost always derive more value from major art museums by spending more time in front of a smaller number of pieces. If you must insist on exhausting yourself by zipping through every single hall just so you can say you "saw everything," then at least do so on a separate visit.