In early May 2007, my wife and I spent 5 days in Paris. We stayed in the Latin Quarter and walked everywhere, so our experience is of a pretty small area.
Before we left I made up a Google map of all the veg friendly restaurants I could find: http://maps.google.com/maps/ms?ie=UTF8&hl=en&msa=0&msid=105265719157739159251.0000011240e475debbede
Here are the restaurants I went to (I would rank them in this order):
I also tried to go to this restaurant in Montmarte, but it was not open at that time:
You can find falafel places around. I found a good one on Rue Saint Jacques just north of Rue Gay-Lusac. There are also some on Rue de La Huchette (a block from the river), and on Rue des Rosiers.
Breakfast is the toughest, but I just found cereal and soy milk at a grocery store and ate at the hotel.