Ah, Paris (spoken with a French accent). I've been to Paris a couple of times. Never had a problem taking pictures. Keep an eye out for pickpockets though, just like in any city. The only thing might be that you will be mistaken for an illegal street vendor, taking pictures from tourists and selling them. As long as you can explain that's not the case, you'll be fine. Using a trypod is fine, just don't setup light deflectors or anything like that . A rangefinder doesn't look that suspicious.
About the eiffel tower (you're probably going to photograph the eiffel tower): everybody goes across the river Seine to Trocadero garden, up to the palace steps, to take a picture of the tower. It's the standard picture you find in every postcard store. Why not take a side street and make a picture thrue a side street?
The best way to travel is the metro. With the 2 and 6 you can go all the way around the city center, mainly above ground. North of the river Seine is the old city, south is more trendy. I don't know what your interests are, I might give you a few places you could visit. Have fun in Paris.