As for Paris, the most obvious places for a first visit include Notre Dame, the Louvre, Montmartre, the Champs-Élysées and the Arc de Triomphe (floodlit at night probably photographs better). Musee D'Orsay has also been mentioned, and is highly recommended, however it's obviously best for looking at paintings rather than taking pictures.
If you're looking for something a little more unusual, try the Père Lachaise Cemetery, host to a huge number of famous people and interesting memorials - everyone from Jim Morrison, Edith Piaf to Oscar Wilde are there to be found. Continuing the death theme, you might also consider the Paris Catacombs, with it's caverns of walls of carefully arranged bones.
Les Invalides, which includes complex of museums devoted to the military history of France (look out for the chest plate from Waterloo punctured through by a cannonball, and the great coat preserved as it was taken off, still covered in the mud from the trenches of the First World War), also makes for an interesting visit - for a really dramatic moment (and photograph), visit Napoleon's tomb which can be found there. The bridge crossing the Seine that leads up to Les Invalides is also one of the most decorated in Paris - sorry, I can't remember its name.
From the top of my head, one other building you might appreciate is the Pantheon Paris - it used to have a Faucault's pendulum (and maybe still does). In it's crypt are several French people, including Victor Hugo, Voltaire and Marie Curie. Hm, there we are, back to death again.
My one tip on gear would be not to bother with a tripod - it'll weigh you down badly, be awkward to carry, and where you might want to use one (for example, inside dimly light buildings), it'll either be not appropriate, or you can find a nearby surface to rest against. I like to travel with what I can fit in my pockets, so no struggling with getting things into or out of bags. So one camera + lens round my neck, and 2 alternative lenses in 2 pockets. You might like to have more with you, then select what you need for each day, according to the itinery. My "standard" is 17-40mm, 70-300mm (fits in a generous pocket!), and 24-70mm round my neck. I might swap the 70-300mm for 8-15mm if I'm going to be inside all day, or 100mm macro if there's going to be something suitable (e.g. gardens).