We were there for 2 weeks in August. You are severely time constrained for Paris. Naturally, I can only advise what we personally found interesting.
For photography opportunities I strongly urge you to visit the Montmartre
http://www.nightstreets.com/p923864946 area because of the character of the area. If you take the underground to Pigallie there is a tram ride leaving from in front of the Moulin Rouge to the top of the hill. About a half mile surrounding the cathedral at the top is solid with small streets and interesting sidewalk cafes and shops. Great place to photograph. We spent two days there.
Notre Dame and the area to it's north. Just south of Notre Dame and across the river is an interesting area of similar character anchored on the south by the Cluny. All very photogenic.
All the tourist areas are awash with people carrying clipboards and wanting you to sign citations while their friends steal your stuff. Firmly tell anybody with a clipboard to go away.
The big name stuff should be further down your list from a photographic standpoint. I'd suggest skipping the Eiffel Tower, the Louvre, and all the museums because they are time consuming. The Tuileries are not very photographic. Neither is walking from the Louvre to the Are Du Triomphe.
My 2015 France gallery is at
http://www.nightstreets.com/f547205863 and you might see an area in it you like.
Post pictures when you get back.
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http://www.nightstreets.com
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"Sick cultures show a complex of symptoms such as you have named...but a dying culture invariable exhibits personal rudeness. Bad manners. Lack of consideration for others in minor matters. A loss of politeness, of gentle manners is more significant than a riot."
This symptom is especially serious in that an individual displaying it never thinks of it as a sign of ill health but as proof of his/her strength. ...Friday, it is too late to save this culture--this worldwide culture... Therefore we must now prepare the monasteries for the coming Dark Age. Electronic records are too fragile..."
--Robert A. Heinlein in "Friday"