Thank you Vincent, here are a few tips for Paris :
1) first and most important : walk, walk, walk, lots of great picture opportunities all over the ciy but visitors have sometimes the tendency to take the metro too go from one site to the other which is understandable. Of course walk with your camera mounted on your hand as you mentionned.
2) be selective in your portraits, use common sense if you are going to take shots of strangers. Most react well, but some not.
3) get out of the main tourisitic sites, otherwise you will only get cliches pictures. Usually by just walking a few streets of the common touristic trails, you see the real life of Paris.
I know you want to travel light, but a 15 or 21mm for Paris would be great .... 😀