Depends on what scene you're into. For such a short time frame I would not recommend going up the Eiffel tower or the Arc de Triomphe because you would waste hours waiting in line. If you want to just take in the big sights just start at the Eiffel tower then walk over to the Seine. Walk up and down the Seine on each side and you'll see most of the big sites including the Musee D'Orsay (pretty nice art gallery inside that isn't as busy as the Louvre, if you're into that. . . it also has "The origin of the world" painting hehe) all the way to Notre Dame Cathedral. That would be a lot of walking but would be do able within a day. If you choose to go into the Louvre, buy your entrance ticket from one of the automated machines instead of from a cashier. The machines are almost hidden, so many people miss them. Montmartre is worth seeing if you feel like taking the metro away from downtown.
What area are you staying in? I might be able to help you more exactly then.
The north part of the Seine has some sketchy places after dark but, since you're an international man of mystery, I doubt you have to worry.
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